Physics Year 12 Notes

Module 6 Electromagnetsm

IQ: What happens to statonary and moving charged partcles when they interact with

an electric or magnetc feld?

Statonary charged yartcles do not elyerience a force in a magnetc feld ( = qvBsinθ), but they do

elyerience a force in an electric feld ( = qE). Moving charged yartcles elyerience a force both in a

magnetc feld and in an electric feld. +f a charged obedect is yroedected into the feld it iill elyerience

a force acceleraton through change in syeed, directon or both) as a moving charged obedect eg:

current) induces a magnetc feld as yer Amyere-Maliell lai thus, the tio felds iill interact iith

each other. Similarly, moving and statonary massive yartcles in a gravitatonal feld elyerience a

force.

Charged yartcles yroedected into a uniform E feld have a yarabolic traedectory or undergo UCM.

(ields are illustrated using lines travelling from + to – E feld) or North to South B feld). (or D

uniform felds going into the yage, feld lines are illustrated by evenly syaced crosses. (or uniform

felds coming out of the yage they are illustrated by evenly syaced dots. Strength of the feld is

denoted by density of the lines. B feld lines aliays form looys.

Electrical (ield V/m)

E feld strength scalar version of E feld) at a yoint in syace is defned as the electrical force () actng

on a yositvely charged test yartcle divided by magnitude of the test charge q). iiven by:

E = (/q ihere E is electric feld strength N/C or V/m), ( is force on yoint charge ( and q is charge of

yoint charge C)

To fnd force on charge in given feld:

( = qE

A uniform electric feld is given by:

E = V/d ihere V is yotental diierence V), d is distance betieen yarallel ylates m) and E is electric

feld strength N/C or V/m)

Coulomb’s Law

(orce betieen tio yoint charges is given by:

F=¿ {1 } {4 π ε0 }¿ {q1q2} {r

2 } ihere q1 and q2 are the charges C), r is distance betieen the charges

m), ε0 is yermittivity of free syace 8.85 l 10-12) changes deyendent of surrounding material

Electrical Potental Energy (U)

U is the yotental energy of a charged yartcle due to its yositon in an E feld. +f the electrical

yotental energy of a charge = U, this means the E feld can do an amount of iork on the charge = U.

We usually set U = 0.

W = ∆KE = -∆U iork done on charge is equivalent to the negatve of the change in electrical

yotental energy of the charge

Hoi is iork done by the E feldd

1. E (ield ayylied

2. Electrical force acts on charge ( = qE)

. Charge accelerates and velocity increases a = (/m = qE/m, v = u + at)

4. KE increases and U decreases

As yer the Lai of Conservaton of Energy, ihich states that energy cannot be created nor destroyed,

only transformed:

+f iork is done by the feld ak a yartcle moves in directon of feld, k inetc energy increases W = qEd)

ihile electrical yotental energy of the yartcle decreases.

+f iork done against the feld ak a yartcle moves oyyosite to the directon of the feld, the yartclees

electrical yotental energy increases ihile k inetc energy decreases.

A more charged obedect has higher yotental energy.

Force and Displacement Work (W = qV =qEd = 1/2mv2)

KE (KE = 1/2mv2) Velocity U (UE = K.q1q2/r)

Same directon yartcle moves in directon of feld)

Positve iork +ncreases +ncreases Decreases

Oyyosite directon yartcle moves oyyosite to directon of the feld)

Negatve iork Decreases Decreases

+ncreases

Potental Diference (V)

V is iork done yer unit charge in moving a charge betieen 2 yoints. iiven by:

V = W/q ihere V is yotental diierence V), W is iork J), q is charge C)

1 edoule of iork is done on every coulomb of charge that yasses betieen tio yoints.

2D moton

(or moton yarallel to the E feld:

a = qE/m ihere a is acceleraton ms-2), E is electric feld N/C), m is mass k g), q is charge C)

(or moton yeryendicular to the E feld, there is no acceleraton a⊥= 0)

Perpendicular Components Parallel Components

v⊥ = u⊥ v∥2 = u∥

2+ 2a∥∆s∥

∆s⊥ = u⊥t ∆s = u∥t +1/2 u∥2

v∥ = u∥ + a∥t

Magnetc (ield B)

Magnetc felds elist around magnets and moving charges. B felds aliays leave the north yole and

enter the south yole.

Magnetc feld due to a long, straight current carrying iire is given by: B = μ0+/2πr, ihere B is

magnetc feld T), μ0 is yermeability of free syace 4� l 10-7 m/A) deyendent on surrounding

material, + is current A), r is distance from the iire m).

As current increases, strength of the magnetc feld increases.

As distance from the iire decreases, strength of the magnetc force increases.

The magnetc feld is magnetc force yer unit current, yer unit length on a current carrying iire in a

magnetc feld.

RHR for magnetc feld line directon in current carrying wire:

Thumb yoints in the directon of the current conventonal)

(ingers iray around the iire and shoi the directon of the magnetc feld

Magnetc Force on a Moving Caarge

The directon of the force on a charged yartcle in a feld and its acceleraton, is yeryendicular to the

directon of its velocity. The magnitude of this magnetc force is given by:

( = qv⊥B or ( = qvBsinθ ihere ( is the force on the yartcle N), v is velocity m/s), B is magnetc feld

T), θ is angle betieen velocity vector and magnetc feld vector

What factors determine the magnitude of the forced

the comyonent of the velocity at right angles to the feld

the charge

the feld strength

( is yroyortonal to q, B, sinθ

RHR for caarged partcle/current in magnetc feld perpendicularly:

Place fngers in the directon of the magnetc feld B)

Thumb yoints in directon of velocity V) ihich is in directon of conventonal current + to -)

NOT ELECTRON (LOW

Directon of force () on a positve caarge is shoin by the directon your yalm is facing

oyyosite for negatve charge)

+f a force is ayylied yeryendicular to the velocity vector, it cannot mak e it syeed uy or sloi doin – it

can only mak e it change directon in directon of ihich the force ias ayylied thus, causing

acceleraton.

The directon of the force is determined using the RHR. The directon of the force ( is aliays

yeryendicular to the yartclees velocity causing the yath to curve at a constant rate undergoing UCM.

The yath of a charged yartcle iith moton yeryendicular to the uniform magnetc feld is circular.

Hoiever, it cannot travel in a full circle as the centre is out of the feld.

Uniform Circular Moton for Caarged Partcle in a B Field

(c = mv2/r ihere (c is centriyetal force N), m is mass k g), v is velocity m/s), r is radius m)

But centriyetal force = magnetc force

∴ (c = qvB

mv2/r = qvB

Hence, radius of the yartclees yath is given by:

r = mv/qB note: v cancels)

What factors infuence rd

Radius is directly yroyortonal to mass and velocity

Radius is inversely yroyortonal to the charge and magnetc feld strength

Elamyle:

A yroton and electron iould elyerience the same force, but iould have a diierent radius ihen

fred at the same velocity due to mass diierence.

IQ: Under what circumstances is a force produced on a current-carrying conductor in a

magnetc feld?

Motor Eiect

Current is given by:

+ = q/∆t total charge yassing a yoint yer unit tme, moving from yositve to negatve)

A current carrying conductor ylaced in a magnetc feld iill elyerience a force due to the B feld

generated by moving charged yartcles current) interactng iith the elternal B feld. This force is

given by:

( = Bi⊥L or ( = BiLsinθ ihere ( is force on conductor N), B is magnetc feld T), +⊥ is current running

yeryendicular to B feld, + is current, L is length of conductor in B feld m) diameter ihen looy), θ is

angle betieen current carrying iire vector and B feld vector.

+f the current runs yarallel to the B feld, the force = 0.

(orce is at malimum ihen current is yeryendicular to the B feld θ is 90o)

The motor eiect is used to convert electric yotental energy to k inetc energy.

Elamyle:

Used in syeak ers ihere a current foi through a coil of iire irayyed around the cone in front of a

large magnet. The coil is alternately atracted and reyelled by the magnet, this mak es the syeak er

cone oscillate thus, yroducing soundiaves.

RHR for currents in magnetc felds:

Thumb shois directon of magnetc force on a yartcle, (

(ingers yoint in directon of current, + and curl in the directon of B

Force between two parallel wires

As a current yroduces a magnetc feld. 2 yarallel conductors ylaced close to each other iould cause

their B felds to interact – elertng forces on each other.

Currents in same directon – forces are mutually atractve and the feld is ieak ened by the

counteracton betieen the iires B = B1 – B2)

Currents in oyyosite directon – forces are mutually reyulsive and the feld in betieen is

strengthened as it is reinforced by having the same directon B = B1 + B2)

(orce is given by:

( = μ0+1+2L/2πr, ihere ( is force betieen yarallel iires N), L is common length of iires m), r is

distance betieen the iires m), + is current A), μ0 is yermeability of free syace.

What factors determine the magnitude of the forced

Distance betieen them – force is inversely yroyortonal to seyaraton distance

Current in both iires – force is directly yroyortonal to the yroduct of currents

Medium conductors are in – magnetc yermeability

Common length of the conductor – force is directly yroyortonal to common length

Wire 1es force on iire 2 is simyly the same but actng in oyyosite directons as yer Neitones rd lai.

Practcal

(or +1 = +2:

( vs + iould be a yarabolic curve

( vs +2 iould be linear ihere m = μ0L/2πr

( vs r iould be a hyyerbola

( vs 1/r iould be linear ihere m = μ0+2L/2π

Amyerees yarallel iire elyeriment is hoi the value of the Amyere ias defned in 1954.

‘The ampere (1A) is that constant current which, if maintained in two straight parallel conductors of

infnite length, of negligible circular cross-secton, and placed 1 metre apart in a vacuum, would

produce between these conductors a force equal to 2 × 10−7 newton per metre of length.’

Solenoids

B feld of a solenoid is given by:

B = μ0N+/L ihere μ0 is yermeability of free syace 4π l 10-7 Tm/A), N is number of turns, + is current

A), L is length of solenoid m)

Hoi is B infuencedd

Higher number of turns stronger B

Higher current stronger B

Shorter length stronger B

RHR For a solenoid (to fnd current directon or norta pole):

Thumb yoints to north yole

(ingers iray around the iire and shoi directon of the current

IQ: How has knowledge about the Motor Efect been applied to technological

advances?

Torque

Torque is a tiistng force about an alis given by:

� = r⊥( = r(sinθ ihere � is torque Nm), r is distance from alis of rotaton D)/yivot yoint 2D) to

yoint ihere force is ayylied m), r⊥ is yeryendicular distance betieen alis of rotaton and force

ayylicaton m), θ is angle betieen force vector directon of force) and r.

+t is due to a force actng on an obedect at a distance from the yivot yoint or alis of rotaton.

Torque is measure of the force that can cause obedect to rotate about an alis and is a vector quantty

deyendent on force directon.

Hoi is torque infuencedd

A longer r higher torque less ( needed for same rotaton/iork

A shorter r loier torque higher ( needed for same rotaton/iork

R and � are directly yroyortonal double the distance, double the torque

When θ = 90o, torque is at malimum value

RHR for fnding directon of a torque:

(ingers yoint in the directon of the line edoining the yivot yoint and yoint of force ayylicaton

Noi curl fngers in the directon of the force

Your thumb yoints in the directon of the torque vector and fngers shoi the directon of the

resultng rotaton

The torque vector is yeryendicular to the directon of rotaton.

Torque on a current carrying looy in a magnetc feld

Torque is elerted on a current carrying looy in a B feld as the force elyerienced by each end of the

coil oyyoses each other, causing the looy to rotate about the central alis.

� = n+AB sinθ ihere n is number of looys, + is current A), A is area of the looy m2), B is magnetc

feld T), θ is angle betieen normal to the ylane of the coil and feld

Torque is malimised ihen the coil is yarallel to the B feld ak a horizontal θ = 90o as normal

is yeryendicular to B feld) given by:

� = nB+A

Torque is 0 ihen coil is yeryendicular to the B feld θ = 0o as normal is yarallel to B feld)

Understanding DC Motors

A DC motor converts electrical yotental energy to k inetc energy using a current carrying coil in a

magnetc feld.

1. DC is suyylied to the motor

2. The coil elyeriences torque � = n+AB sinθ) due to the interacton of the elternal B feld iith

the currentes B feld ( = BiLsinθ) that ayylies yeryendicular forces to oyyosite ends of the

coil, mak ing the coil rotate.

. The coil reaches the halfiay yoint θ = 0o, normal is yarallel) and inerta allois the coil to

yass the vertcal yositon.

4. Sylit ring commutator reverses directon of the current so that torque contnues in the same

directon and coil rotates to comylete a full revoluton

They iork on 1 yhase.

Components:

Stator - statonary

- Motor casing

- Curved magnets/electromagnets

- +nyut iires

(igure 1 (orce and torque on coil as functon of tme, torque fuctuates betieen 0 and malimum value

- Carbon brushes

- Stator coils

Rotor - rotates

- Armature

- Rotor coils

- Sylit ring commutator

Part Descripton Role

Stator A yair of curved yermanent magnets

Tio yermanent magnets onoyyosite sides of the motor, iith oyyosite yoles facing each other. The yole faces are curved to ft around the armature.

Suyyly the magnetc feld ihich interacts iith the current in the armature/rotor coil to yroducethe motor eiect. Magnetc yole yieces are usually curvedto yroduce a uniformly radial magnetc feld. This ensures that the ylane of the coil is aliays yeryendicular to the B feld, yroducing malimum torque at all angles.

Stator coils yair of electromagnet coils)

Pair s) of coils irayyed around curved laminated iron cores atached to the casing of the motor. The coils are shayed to ft around the armature.

Produces a magnetc feld similar to that yrovided by a yair of yermanent magnets. The iron core concentrates the feld. EM magnets can be made to give a stronger B feld than yermanent magnet of same dimensions.

Rotor Alle A cylindrical bar of metal yassing through the centre of the armature and the commutator.

Provides alis of rotaton for torque to occur. Allois you touse the rotaton ak a outyut device.

Armature Sof laminated sheets of iron of ihich the turns are iound around.

Carries the rotor coils. Enhances the magnetc feld of the rotor, leading to greater torque. +t is laminatedto break uy the eddy currentsto increase energy efciency.

Rotor coils Also called the armature orrotor. Multyle coils at angles to each other iound around a sof iron core. There may be one, in a very simyle motor, or several coils. The ends of the coils are connected to bars on the commutator.

The coils yrovide torque, as the current yassing through the coils interacts iith the magnetc feld. As the coils are mounted frmly on the rotor, any torque actng on the coils is transferred to the rotor hence, the alle. The armature usually has multyle turns ‘ne iound around a sof iron core to have a stronger magnetc feld due to a greater magnetc yermeability

thus, a stronger torque. A steadier torque is yroduced using multyle coils at angles/yeryendicular to each other.

Contacts

Sylit ring commutator Conductng ring of metal mounted on the alle at one end of the armature, and cut into an even number of seyarate bars tio in a simyle motor). Each oyyosite yair of bars is connected to one coil.

Reverses current directon in the coil every half a rotaton through short circuitng to maintain a constant torque directon.

Brushes Comyressed carbon block s,connected to the elternal circuit and yart of the stator. They are mounted on oyyosite sides of the commutator and syring-loaded to mak e close contact iith the commutator bars.

Provides sliding electrical contact to the commutator/coil and connects to the elternal yoier suyyly

Drawing a DC motor:

Problems wita a brusaed DC Motor:

Brushes iear out and need reylacement

Commutator is easily iorn thus, shortening motor life

Syark ing at the commutator can be a hazard

IQ: How are electric and magnetc felds related? (Overlap)

Magnetc (lul

Magnetc ful is a measure of the amount of magnetc feld B) yassing through a given area A),

visualised as the number of feld lines yassing through an area. +t is given the symbol yhi ‘Φ ‘and is

measured in Webers Wb) or Tm2. +t is given by:

Φ = B∥A = BAcosθ ihere Φ is magnetc ful Wb), B is magnetc feld T), B∥ is comyonent of B feld

yarallel to normal of the coil yeryendicular to ylane of the coil), A is surface area m2), θ is the angle

betieen B feld vector and normal to tae area.

Φ is infuenced by:

Magnetc feld strength/ful density B) higher B higher Φ change either strength of

magnet or distance from B feld)

Area of looy A)

Angle of looy to the magnetc feld θ)

Φ is at a malimum ihen the feld is yeryendicular to area/ylane of the coil θ = 0o as normal

is yarallel to B feld)

Φ = 0 ihen θ = 90o and feld is yarallel to area of the coil θ = 90o)

(lul is a scalar quantty. +f yositve ful decreases then change in ful is negatve ihereas if yositve

ful increases the change of ful is yositve.

Flux of Rotatng Coil

When coil is yarallel to feld lines horizontal) then there is no ful as there are no ful lines going

through the coil θ = 90o). +f coil is rotated by 180o, ful lines have rotated 180o relatve to the coil.

irayh of Φ vs t iould have a sinusoidal relatonshiy

Magnitude of EM( is greatest ihen the Φ vs t functon crosses the l alis.

(aradayes Lai – EM inducton

When a conductor elyeriences changing magnetc ful, a voltage iill be induced ε). +f a voltage is

induced in a closed circuit, a current iill foi. This is called electromagnetc inducton. Magnetc ful

changes if area of the looy changes, angle betieen the looy and the B feld changes or magnetc

feld in a closed circuit, a current iill foi. This is called electromagnetc inducton. Magnetc ful

(igure 2 irayh ihen looy starts at vertcal yositon

Figure 1 Graphs when loop starts at a horizontal positon

changes if area of the looy changes, angle betieen the looy and the B feld changes or magnetc

feld strength changes.

EM( induced in a moving conductor is given by:

ε = BLV = BLVsinθ ihere ε is induced EM( V), B is the magnetc feld strength Wb), L is length of

conductor m), V is velocity of the conductores movement in and out of the feld m/s) multyly by

number of looys

RHR For a conductng rod in a B feld:

V =directon of inyut of yositve charged yartcles moving conductor) is the thumb

( = directon of force directon of voltage) is the yalm

B = magnetc feld lines are the fngers

(aradayes elyeriments:

+nducton iith a magnet – Relatve moton betieen a magnet and coil causes a change in Φ

inducing an EM(

+nducton iith coils – AC current in a yrimary coil causes a changing Φ, inducing a changing

EM( in a secondary coil

+nduced EM( in a circuit caused by changing ful is given by (aradayes Lai of +nducton:

ε = -N ∆Φ/∆t) ihere ε is the voltage or EM( V), N is number of turns, ∆Φ is change in magnetc ful

Wb), ∆t is change in tme s)

Equaton has a negatve due to Lenzes Lai ihich states that an induced EM( creates a B feld that

oyyoses the moton that induced it in the frst ylace as yer the Lai of Conservaton of Energy.

As Φ = BAcosθ,

ε = -N ∆BAcosθ)/∆t ihere B is magnetc feld T), A is surface area m2), θ is the angle betieen B

feld vector and normal to tae area, ∆t is change in tme s)

ε is infuenced by:

(igure 4 Positve charges elyerience an uyiards force as yer RHR ihile electrons elyerience a doiniards force. This seyarates the yositve and negatve charges in the conductor causing a yotental diierence betieen the tio ends of the conductor ak a inducing EM(

Magnitude of change in magnetc ful higher change higher EM( direct)

Number of turns of coil larger no. of turns higher EM( induced direct)

Length of tme over ihich change occurs shorter tme/higher frequency higher EM(

inversely yroyortonal)

When the looy fully enters the B feld, the voltage at the yositve and negatve terminals are the

same on both sides on the looy thus, there is no EM( generated thus, no current foiing. +f a looy

moves iithin a uniform B feld, there iill be minimal change in the number of ful lines in the looy

thus, no EM( is generated and no current fois.

We can tak e any yarameter k eyt constant out of the brack et eg: ε = -Acosθ B f - Bi)/∆t if area and

angle remain constant

QualitatvePractcal

QuanttatvePractcal

Investgaton 1

1. Connected air core solenoid to centre reading galvanometer

2. Move bar magnet in and out of the solenoid observe eiect on galvanometer

. Use RHi rule to determine directon of the current

4. Vary the syeed and observe changes

Voltage is a form of EM(, but not all EM( are yotental diierences as EM( accounts for yath tak en

ihereas yotental diierence does not. EM( is a scalar quantty.

Lenzes Lai

Lenzes Lai is a manifestaton of the lai of conservaton of energy. +t states that an induced EM( acts

to yroduce an induced current that has an associated B feld that oyyoses the original change in ful

that induced the EM( oyyoses moton). Current must foi in a directon that reduces the magnetc

ful through the looy and reduces rate of ful change.

Elamyle:

As solenoid ayyroaches a magnet iith a north yole closest to it, current iill foi to create a feld

iith a north yole toiards the magnet use solenoid RHR) hence, reyelling the magnet.

+f solenoid is leaving a magnet iith a north yole closest to it, current iill foi to create a feld iith a

south yole toiards the magnet use solenoid RHR) to sloi doin the change in ful by atractng the

magnet.

Eddy Currents

Eddy currents are induced currents formed in bulk yieces of metal due to an elyerience of changing

magnetc ful and the yiece of metal forming a closed circuit. Directon of current foi is determined

by solenoid RHR and Lenzes Lai ihere the current fois to form a B feld that oyyoses the change in

magnetc ful.

Practcal

Investgaton:

A: As the ylate enters the feld, the changing magnetc ful creates an induced EM(. Eddy currents

circulatng free electrons in metal caused by the induced EM() are created. According to Lenzes lai,

the directon of the eddy currents must oyyose the change that causes them.

The eddy currents yroduce eiectve magnetc yoles lik e a solenoid) on the ylate, ihich are

reyelled or atracted by the yoles of the magnet, thus giving rise to a retarding force that

oyyoses the moton of the yendulum.

B: The slots cut out from the metal ylate restrict the foi of eddy current iith insulatng air. The

magnetc yoles the eddy current creates are thereby ieak ened as are the retarding forces elerted

on them by the elternal feld. The eddy currents formed are more localised and therefore restricted.

Real Life Applicatons

Recreatonal equiyment

Railroad train brak ing system

Rollercoaster brak ing system

+ndustrial equiyment - Emergency brak ing of

dangerous equiyment

iym equiyment

- Used in roiing machines to change resistance

- Allois for smooth transitons betieen resistance levels

Problems wita Eddy Currents

Eddy currents are ofen undesirable as they dissiyate energy in the form of heat. To reduce energy

loss, the moving conductor yarts are ofen laminated. A conductor is laminated by slicing it into thin

sectons and seyaratng each one iith insulatng ylastc) layers.

+t is eiectve ihen the laminatons are yeryendicular to the ylane of the eddy current.

ienerators

An AC generator converts k inetc energy to electrical yotental energy in the form of alternatng

current AC). The coil is atached to an armature/rotor that rotates in the B feld betieen the

magnets. As the coil rotates, the magnetc ful in the looy changes thus, inducing an EM( across the

ends of the coil ε = -N∆Φ/∆t). The ends are atached to conductng sliy rings that rotate iith the coil

and contact the brushes. The brushes connect to an elternal circuit ihere the EM( or current is

used.

Comyonents of an AC generator:

Pair of magnets

Armature

Rotor coils

Sliy rings – tio circular metal rings mounted on end of the armature that are connected to

the tio ends of the coil. The rings rotate iith the coil and contact the brushes.

Brushes

Alle

RHR (rigat aand pusa rule) for generators:

Thumb yoints in the directon of ihere the side iill rotate thumb directon of inyut moton)

Palm is directon of the current or force on moving yartcles

(ingers are magnetc feld

Drawing a simple AC generator

The natural outyut of a rotatng coil is AC as current siitches directon every half turn. To mak e the

outyut DC, a sylit ring commutator can be used.

Malimum EM( outyut for an AC generator is given by εmal= 2πfnBA ihere f is frequency rotatons

yer second, n is number of turns, B is magnetc feld and A is area.

+ = V/R as yer Ohmes Lai.

DC Generator

A DC generator converts the outyut EM( of the generator so that the EM( is aliays yositve. +t does

so by using a sylit ring commutator ihich reverses the current foi in the external circuit every

aalf-turn, instead of sliy rings. The outyut is yulsed, so multyle coils are used to yrovide a steady

current.

Back EM(

+n an electrical motor, current is suyylied to a coil in a B feld ihich elyeriences a force as yer the

motor eiect thus, turning. Hoiever, the coil is elyeriencing a constantly changing magnetc ful due

to rotaton relatve to the B feld and (aradayes Lai states that a changing magnetc ful induces an

EM( in a conductor. As a result, the self-generated EM( yroduced in the motor oyyoses the inyut

EM( as yer Lenzes Lai. This is called the Back EM(.

Back EM( refects the lai of the conservaton of energy in that it can never elceed inyut EM(.

Back EMF and Current

The net EM( that causes the current in the coil is a result of the diierence betieen the inyut EM(

and back EM(.

As yer Ohmes Lai, P = V+, a higher back EM( causes a loier current given a constant P.

Influences on Back EMF:

As rotaton syeed increases back EM( increases direct)

As inyut EM( increases back EM( increases direct)

As load increases more iork is done/more yoier used coil rotates sloier back

EM( decreases inverse)

Inrusa Current Limitng

+nrush current hayyens ihen there is a lag of back EM( at the start thus, causing a syik e in current

initally before the motor starts syinning. The syik e in current can cause the motor to overheat and

burnout. To yrotect the motor, a variable resistor is used on start-uy and removed as the coiles

syeed increases.

AC +nducton Motors

The AC inducton motor converts electrical yotental energy to k inetc energy through emyloying

(araday and Lenzes Lai. Unlik e, DC motors, it oyerates on a -yhase yoier suyyly consistng of

seyarate circuits of AC.

Comyonents of an AC inducton motor:

Stator

o Multyle yairs north and south yole) of electromagnetc coils stator coils) ihere

each yair is connected to a diierent circuit 1 yhase of the -yhase yoier suyyly)

Rotor

o Squirrel cage – a cage made of conductng bars connected to tio conductng rings

on either side

o Alle

o Laminated iron core

Note: there are no sliy rings or brushes

1. Stator coils are connected to a yhase AC yoier suyyly 120o of a revoluton out of yhase)

ihich yroduces a rotatng magnetc feld thus, yroviding the change in magnetc ful needed

for inducton to occur (aradayes Lai)

2. The changing magnetc ful induces an EM( in the squirrel cage rotor ihich is a conductor

ε= -N∆Φ/∆t). As the squirrel cage forms a closed circuit that is shorted by the end rings), a

current fois.

. As yer Lenzes Lai, the current fois to form a B feld that oyyoses the inital change in ful

thus, the squirrel cage rotor atracts the rotatng magnetc feld thus, causing it to

elyerience a torque in the directon of the rotatng B feld

4. They are also current carrying conductors in a magnetc feld, so they elyerience a force due

to the motor eiect, ihich leads to torque.

The rate of rotaton of a rotor of an inducton motor is aliays less than the rate of rotaton of the

stator feld due to a natural lag not synchronous syeed) k noin as sliy that causes the change in ful

that mak es the motor iork .

yhase inducton motor yroduces a more sustained torque but, 2 yhase inducton motors also iork

albeit, rotaton is half-turn by half-turn rather than a smooth rotaton.

With a load, the torque of an inducton motor increases due to higher current) and syeed

decreases.

AC DC

Loi yoier demand on start Controllable acceleraton Controlled start current Reduced yoier line disturbances Longer life tme Adedustable oyeratonal syeed Adedustable torque limit Simyle in constructon Cheayer More yoierful

+nduced current, no direct electrical connectonCan be synchronous rotors synchronised iith frequency of suyyly current and used ihen syeed needs to be constant under various loads, generally brushed) or inducton use EM inducton to yroduce torque, most common AC motor and can be single or three yhases, imyortant in industry due to their load cayacity)

Easy installaton Syeed control over iide range Quick startng, stoyying, reversing and

acceleraton Highs startng torque Linear syeed torque Widely used in small ayyliances Does not require you to be on the grid Can be brushed or brushless longer

lifesyan, use sensors to detect rotor yositon)

Use DC inyut

Shaded yole single yhase AC inducton motor:

htys://iii.youtube.com/iatchdv=urfyZo1ed9y+

IQ: How are electric and magnetc felds related?

Transformers

A transformer +s an electrical device that transfers electrical energy from one circuit to another via

EM inducton. A transformer can acceyt energy at one voltage and deliver it at another.

A transformer consists of tio solenoids ylaced near each other conventonally, iound around the

same iron core) so that an AC current in the yrimary coil induces a current in the second coil ε =

-N∆Φ/∆t). As an AC current changes directon, the magnetc ful changes hence, an EM( is induced

as yer (aradayes Lai. As the secondary coil is also a closed circuit, an AC current iith the same

yeriod is induced.

The yrimary coil is the inyut coil and the secondary coil is the outyut coil.

(lul link age

(lul link age is hoi much ful from the yrimary coiles B feld yasses through the secondary coil. Coils

need to be matched so that a change in ful in one coil causes a change in ful in another.

There are tio iays of doing this: coils can share the same syace by ylacing one inside the other or

they can share the same ferromagnetc core. Tae second metaod works tae best as the yrimary

coiles current magnetses the full core thus, yroviding ful link age betieen the yrimary and

secondary coil.

An ideal transformer assumes that ful link age is yerfect no ful leak age) so that ful through any

looy is same for both coils, no energy is lost.

Stey-uy and Stey-doin Transformers

Converts inyut alternatng voltage to a higher ‘stey uye voltage or loier ‘stey doine voltage.

A stey-uy transformer has a greater number of turns on the secondary coil. They are used ihen a

greater voltage is required such as at yoier statons. To not violate the lai of conservaton of

energy, Pin = Pout thus, as voltage increases, current must decrease P = V+).

A stey-doin transformer is used to decrease voltage AC is used instead of DC in transformers. +t has

a greater number of turns on the yrimary coil hence, as voltage decreases, current must increase for

P to stay constant. Phone chargers use these transformers to decrease the suyyly voltage to that

needed by the yhone.

Relatonsaip between primary and secondary coils is given by:

Vs/Vy = Ns/Ny ihere Vy is voltage of yrimary coil/inyut voltage V), Vs is voltage of secondary

coil/outyut voltage V), Ny is number of turns on yrimary coil, Ns is number turns on secondary coil.

Pin = +yVy=+sVs=Pout thus, +y/+s = Ns/Ny = Vs/Vy

+f Ny> Ns then Vy > Vs thus, stey-doin

+f Ny < Ns then Vy < Vs thus, stey-uy

Real Transformers

+deal transformers mak e 2 assumytons. One being that the ful link age is yerfect so that the ful

going through the frst coil is elactly the same as the ful going through the second coil. The second

being that the transformer is 100% efcient and no energy is lost.

+n reality, ful link age is never yerfect and there iill aliays be ‘stray felde. This stray feld can induce

eddy currents in nearby materials causing heatng and vibraton leading to a loss of energy as heat or

sound. Energy is also lost through the heatng of transformer coils and core due to the resistance of

iires or eddy currents iithin the ferromagnetc core. Energy is also lost in the core due to change in

directon of the magnetc feld hysteresis) and the yrocess of de and re-magnetsaton ihich causes

a loss of energy through heatng of the core.

To imyrove transformeres efciency, you can:

Use a ferromagnetc core, reduce distance betieen coils and reduce air gays to reduce ful

leak age

Use loi resistance iire and cooling yrocesses to reduce energy lost as heat

Laminate the ferromagnetc core to minimise eddy currents

Use ‘sofe metal core to reduce energy lost due to Hysteresis

Real Life Applicatons:

Stey-uy transformers are used at yoier statons to increase the voltage to reduce yoier loss during

transmission due to resistance.

Stey-doin transformers are used in electricity substatons to reduce the voltage for consumer use.

Power Loss During Transmission

Poier is lost in transmission lines due to heatng, usually due to resistance. Poier loss is given by:

PLoss = +2R = +∆V = ∆V2/R ihere P is yoier loss W), + is current A), R is resistance Ω), V is voltage V)

Module 5 Advanced Mechanics

IQ: How can models that are used to explain projectle moton be used to analyse and

make predictons?

Proedectle Moton

A yroedectle is an obedect that cannot move by itself, moving freely under the force of gravity.

There is no other force other than gravitatonal force actng on the obedect

Net force of the yroedectle is gravitatonal force mg), ieight

Obedects elyerience:

o Vertcally doiniard force of 9.81 N/k g

o Vertcally doiniard acceleraton of 9.81 ms-2

The yroedectle moves in a yarabolic arc as the vertcal gravitatonal force causes it to deviate from its

otheriise linear yath.

According to Neitones 2nd lai ( = ma), the yroedectlees horizontal comyonent has constant velocity

no acceleraton) as there is no elternal force actng on it the horizontal comyonent is indeyendent

of the vertcal comyonent), it remains moving due to inerta Neitones 1st Lai).

(orce is aliays doiniards, but directon of moton varies.

Whether an obedect is yroedected or edust droyyed, it iill stll fall at the same rate

Assumytons of our model:

Constant vertcal acceleraton due to gravity

Curvature of Earth ignored

No air resistance

Analysing Projectle Moton

Proedectle moton is 2D moton. To analyse:

1. Break uy moton into vertcal and horizontal comyonents

2. The tio comyonents are comyletely indeyendent of each other thus, they can be treated

seyarately

. There is no acceleraton in the horizontal directon as gravity only acts vertcally

4. (ind vertcal and horizontal comyonents

Y comyonents: usinθ, vsinθ, a = 9.81ms-2, vertcal height

X comyonents: ucosθ, vcosθ, a = 0, range

5. (ind tme, as tme is the same for both comyonents

X DIrecton Y Directon

vx = ux ihere v is l comyonent of fnal velocity, u is l comyonent of inital velocity m/s)

vy2 = uy

2+ 2ay∆sy ihere v is y comyonent of fnalvelocity, u is y comyonent of inital velocity m/s), a is vertcal acceleraton of 9.81ms-2, s is y comyonent of disylacement

∆sx = uxt ihere s is l comyonent of disylacement m), t is tme s)

∆sy = uyt +1/2 ayt2 ihere u is y comyonent of

inital velocity m/s), a is vertcal acceleraton of9.81ms-2, s is y comyonent of disylacement, t is tme s)

vy = uy + ayt ihere v is y comyonent of fnal velocity, u is y comyonent of inital velocity m/s), a is vertcal acceleraton of 9.81ms-2, t is tme s)

Special cases:

+f the yroedectle launches and lands at the same height, the inital and fnal angle is the same

magnitude – only one is an angle of elevaton and the other an angle of deyression.

+f there is no angle of launch, velocity in the y directon is zero ihile velocity in the l

directon is the same as inital velocity

Types of Questons

No inital vertcal velocity comyonent/half-fight/no angle

+nital velocity = horizontal velocity = constant

Vertcal velocity is initally zero but increases as obedect falls vy = uy + at)

No inital vertcal disylacement

+nital horizontal velocity =ucosθ = constant

+nital vertcal velocity = usinθ

Sy = 0

Vertcal velocity at mal. height = 0

Launch angle = landing angle

Angle of yroedecton for mal. range = 45o

Proedectle fred at an angle above ground

+nital horizontal velocity =ucosθ = constant

+nital vertcal velocity = usinθ

Vertcal velocity at mal. height = 0

Angle of yroedecton for mal. range = 45o

Half fight yroedectle moton:

Doiniard acceleraton = gravity

Vertcal velocity increases constantly

Horizontal velocity is a constant

(ind:

tme of fight half-fight and full-fight)

o +nfuenced by:

+nital vertcal velocity ONLY +( LAUNCH ANiLE > 0 – increase in inital

velocity longer tme of fight direct)

Launch angle – higher launch angle longer tme of fight direct)

Vertcal disylacement – higher vertcal disylacement longer tme of fight

direct)

inital velocity velocity immediately afer launch)

launch angle

malimum height

o Launch angle – higher launch angle higher malimum height direct)

o +nital vertcal velocity i.e.: faster it is yroedected uyiards the higher it goes,

regardless of the horizontal moton

o Vertcal disylacement – higher vertcal disylacement higher malimum height

direct)

fnal velocity velocity edust before it hits ground)

velocity, height, distance at a yoint in tme

launch height

horizontal range of the yroedectle

o +nfuenced by

Launch angle – increase in angle increase in range UP TO 45o THEN

increase in angle decrease in range

+nital velocity – increase in inital velocity increase in range direct)

Vertcal disylacement – increase in vertcal disylacement increase in

range direct)

The traedectory of a yroedectle is determined by its inital velocity direct relatonshiys) and forces that

act on it as iell as air resistance.

y = usinθ both are deyendent on inital velocity and angle betieen yroedectle and the ground.

l = ucosθ

The malimum height for a yroedectle is the highest yoint of the arc given by: launch height –

usin2l/2g

(light tme for a yroedectle iith same launch and landing height is given by: - 2usinl/g and fnal

velocity iill be equal to inital velocity

Equatons of moton:

s = ut + 1/2at2

v2 = u2 + 2as

v = u + at

Practcal 1: iravitatonal (orce from Pendulum CHECK

Practcal 2: Proedectle Moton

Charged Partcles Proedected into Electric (ields

Similarites to projectle dropped in G feld Diferences to projectle dropped in G feld

+f droyyed, accelerates uniformly yarallel to feld lines+f yroedected, iill folloi yarabolic traedectories in an uniform feld

Diierent masses iill accelerate at diierent rates unlik e in a gravitatonal feld ihere all masses accelerate at the same ratePositve and negatve charges iill accelerate in oyyosite directonsElact curve of a yroedectle in an electric feld is deyendent on velocity, charge and mass, unlik ein a gravitatonal feld ihere all masses if launched elactly the same iill folloi the same curve

(actors that infuence:

Range

o Higher inital velocity larger range direct)

o Larger charge smaller range inverse)

o Larger mass larger range/less defecton direct)

o Higher voltage smaller range inverse

Acceleraton

o Larger charge greater acceleraton direct)

o Smaller mass greater acceleraton inverse)

o Higher voltage greater acceleraton direct)

Lik e yroedectles, y and l velocity comyonents can be found. Equatons of moton can be used.

E = V/d cayital V is voltage) distance betieen ylatesd

IQ: Why do objects move in circles?

Circular Moton

An obedect travelling a circular yathiay at constant tangental syeed is undergoing uniform circular

moton UCM).

Characteristcs of UCM:

Moton along circular yath of radius r

Tangental syeed v is constant hence, yeriod T is constant

Angular velocity rate of change of angle) 𝜔 is constant

Linear velocity is not constant as directon is contnually changing. Linear velocity is

yeryendicular to net force of the obedectes rotaton

Centriyetal acceleraton ac) is directed toiards the centre

Net force (c) toiards the centre of the circle

The net force of an obedect moving in UCM is directed toiards the centre and is called centriyetal

force and is given by:

(c = mv2/r ihere (c is centriyetal force N), m is mass of obedect in circular moton k g), v is

velocity/orbital velocity of the obedect m/s), r is radius of the circle m)

(actors that infuence:

Centriyetal force

o Orbital velocity

There is a direct square relatonshiy. +ncrease in orbital velocity squared

increase in centriyetal force actng on/required to k eey obedect in UCM

increases as iell

o Mass

Mass increase centriyetal needed increases direct)

o Radius

+ncrease in radius decrease in centriyetal force needed/actng on it

inverse)

(ormula Dumy:

T = 1/f ihere T is yeriod tme to comylete one revoluton) s), f is frequency Hz)

𝜔

o 𝜔 = ∆θ/∆t ihere 𝜔 is angular velocity rad/s), θ is angle rad), t is tme s)

o 𝜔 = 2�f ihere f is frequency Hz)

o 𝜔 = ∆s/rt ihere s is arc length m)

o 𝜔 = v/r ihere v linear velocity m/s), r is radius m)

v = 2�rf = r𝜔 = 2πr/T

v = √iM/r ihere v is orbital velocity m/s), i is universal gravitatonal

constant 6.67 l 10-11 Nm2k g-2) average amount of gravity elyerienced in the

universe) , M is mass of central obedect k g), r is orbital radius m) NOT ON

(ORMULA SHEET

ac = r𝜔2 = v2/r derived from ( = ma and (c = mv2/r)

o (or satellites:

(c = mv2/r = mr𝜔2 = mac ihere m is mass k g)

o (or satellites:

(c = iMm/r2 ihere m is mass of syinning obedect k g)

Conditons for an Object to Execute Circular Moton

As the obedect is acceleratng, there must be a net force actng on the obedect given by Neitones 2nd

Lai (=ma) directed toiards the centre.

(net = (c = mv2/r

Elamyles:

Situaton Force providing Fc Conditon

Car driving around a horizontalcircular bend

(ricton betieen the tres and the road f

f =mv2/r

Ball siinging on a string Tension in the string toiards alis of rotaton T

T = mv2/r

Satellite orbitng a ylanet iravitatonal force betieen satellite and ylanet FG

Fg = mv2/r

+f the centriyetal force and details of the moton do not satsfy Fc = mv2/r, then the obedect will not

follow UCM and instead folloi a diierent yath:

Situaton Conditon Moton

Car driving around a horizontalcircular bend

Road is sliyyery, there is not enough fricton f < mv2/r

Car slides out of the turn and travels on a linear yathiay tangent to the circle) d/t inerta

Ball siinging on a string String is cut so no tension in the string, T = 0 < mv2/r

Ball fies oi and travels on a linear yathiay tangent to the

circle) d/t inerta

Satellite orbitng a ylanet Satellites moton does not satsfy conditons of circular moton, Fg ≠ mv2/r

Satellite follois elliytcal orbit

The centriyetal force is aliays yeryendicular to the directon of velocity and has constant strength

desyite changing in directon. The yoyular term ‘centrifugal forcee actually refers to the force of

inerta the syinning obedect elerts on the iall or roye as yer Neitones 1st Lai ihich feels lik e an

outiard force.

Acceleraton and force occur in the same directon. Centriyetal acceleraton occurs due to a

constantly changing directon NOT because of the velocity, as magnitude of the velocity does not

change.

RPM rad/s by convertng minutes to seconds by dividing by 60 and convertng revolutons to

radians by multylying by 2π

k m/hr m/s by dividing by .6

Analyse forces on an object executng uniform circular moton

1. +dentfy forces actng on the obedect. Drai a free body diagram.

2. Determine directon of acceleraton. (or UCM, acceleraton is aliays toiards centre of the

circle

. Decomyose the forces into yarallel and yeryendicular comyonents to acceleraton)

4. Ayyle Neitones 2nd Lai to comyonents and fnd the unk noin

a. +n the directon of acceleraton there is a net force: (net = mv2/r

b. Peryendicular to acceleraton, a = 0 so (net = 0

c. Ofen fnd ac frst

Uniform circular moton can be ayylied to diierent systems. Three common systems are: car moving

around a corner on a fat and bank ed road and mass on a string conical yendulum).

Cars moving around aorizontal circular bends

(ricton suyylies the centriyetal force to mak e a car go around a bend on a fat surface thus, f = (c =

mv2/r. The normal force and fricton force are on all 4 tres. Therefore, ihen a car corners on a fat

road ie can model the bend as yart of a circle.

(orces actng:

Lateral frictonal force betieen road surface and tres f)

Normal force N)

Weight force i)

The car does not accelerate vertcally uy thus, N = i. Lateral frictonal force can be infuenced by

turning the steering iheel ihich causes the front iheels of the car to angle.

Possible Situatons:

Fc Moton

( = mv2/r UCM

( > mv2/r Car moves toiards the centre of the circle. Radius decreases so car turns more sharyly.

( < mv2/r Car moves aiay from the centre of the circle. Radius increases so car turns more gently.

Way are we learning tais?

The ability of the car driver) to turn a corner deyends on hoi shary it is r) and hoi fast the car is

travelling can be controlled). Sloiing doin, ie can turn a sharyer corner smaller radius).

Due to a direct square relatonshiy, increasing velocity by l1 results in l4 of the (c needed to k eey

the body in UCM. Thus, the faster the car is going, the greater the frictonal force required. There is a

malimum frictonal force that the road can elert on tres thus, sloiing doin is vital. RMS indicates

suggested syeeds for corners.

(ricton yrovided reduces ihen there is iater, oil or iorn tres.

Cars on banked tracks (ignore fricton)

A bank ed road is a road that is tlted into the centre of the turn or circular yath. This results in a net

force that accelerates the car in the directon of the corner, helying vehicles travel at higher syeeds

around corners iithout sk idding. Since the car is moving around a corner, ie can model this as an

arc of a circle thus, (net = (c. This situaton look s similar but, is diferent to an inclined plane queston

in that the normal force is the HYPOTENEUSE mg = Ncosθ) rather than a vertcal side N = mgcosθ)

i.e. tae triangles are diferent.

Way is tais?

On an inclined ylane as the angle increases, the normal force decreases as more and more of the

ieight is suyyorted by fricton. But, on a bank ed curve as the sloye increases, the normal force

needed increases as the centriyetal force increases e.g. a racetrack this corresyonds to the steeyest

bank ed curves being at the sharyest/tghtest corners. The sharyer the corner the more centriyetal

force is required to mak e the turn, requiring more bank ing and more normal force.

(orces actng:

Normal force N) - tlted toiards centre and

comyonent toiards centre contributes to (c

Weight force i)

+f the car is turning at the design syeed, the aorizontal

component of tae normal force provides Fc rather than

fricton f)

Design Speed

X

Y

Design syeed is the syeed required for the car to not slide uy or doin the bank ed road. +t requires a

balance betieen forces uy the bank and forces toiards the centre.

+f the syeed is too high then the car iill start moving uy the bank . +f the car is too sloi it iill slide

toiards the centre.

+t is given by: √ rgtanθ) NOT ON (ORMULA SHEET

Analysis: Derivaton of Fnet = Fc = mgtanθ, v = √(rgtanθ), a = gtanθ, θ = tan-1 (v2/rg)

(or centriyetal force, (net = (c = mgtanθ:

sinθ=xN∴x=Nsinθcosθ= y /N∴ y=Ncosθ

But there is no acceleraton in the y directon,

∴Ncosθ=mgN=mg / cosθFnet=NsinθF c=mv2 / r

But,

Fnet=Fc∴Nsinθ=mv2

r¿ :N=mg /cosθmgsinθ / cosθ=mv2 / rmgtanθ=mv2 / r∴Fc=mgtanθ

(or design syeed, v = √ rgtanθ):

mgtanθ=mv2 / rrmgtanθ=mv2v2=rgtanθv=√rgtanθ

(or radius, r = v2/gtanθ:

r=mv2 /mgtanθ¿v2

gtanθ

(or oytmal angle, θ = tan-1 v2/rg):

tanθ=v2 / rgθ=tan−1 (v2 / rg )

(or centriyetal acceleraton, a = gtanθ:

Fnet=ma∴ma=mgtanθa=gtanθ

+t helys the car mak e the turn by adding the comyonent of the ieight force mgtanθ) or normal

force to the fricton thus, increasing centriyetal force

A mass on a string = moton in a aorizontal circle (conical pendulum) eg: totem tennis

The string is at an angle θ from the vertcal. The mass siings in a circular traedectory, draiing a circle

iith radius r) at distance h) beloi the mount. The horizontal comyonent of tension yrovides the

centriyetal force.

(orces actng:

Tension of the string T = mv2/r

θ

Y

X

Weight force i = mg) doin

Analysis and derivaton: sinθ=xT∴x=Tsinθcosθ= y /T∴ y=Tcosθ

As there is no movement in the y directon,

∴Tcosθ=mgT=mg / cosθ

But,Fnet=Fc=Tsinθ¿ :T=mg /cosθFc=mgsinθ /cosθ∴Fc=mgtanθ=mv2/r

Efects of increasing tension:

Vertcal comyonent of T remains constant balances doiniard ieight force angle

increases direct)

Horizontal comyonent increases centriyetal force increases angle increases direct)

Total energy and work done on object undergoing UCM

Kinetc energy K) = ½ mv2

When an obedect is undergoing UCM its magnitude of velocity v) is constant. Thus, k inetc energy is

also constant.

Practcal 1: Centripetal Mass Balance

A centriyetal mass balance is syun on a string. The other end of the string is atached to a hanging

mass �and alloied to slide through a frictonless tube or yulley.

- The mass � is syun at a certain syeed so that the mass � remains statonary.

As M remains statonary,

As the syinning mass is not fuctuatng in height,

On M: T = Mg

On m: Tcosθ = mg

Thus, T = mg/cosθ

Subbing T = Mg

Mg = mg/cosθ

M = m/cosθ

Relatonshiy betieen masses and angle ihich it must rotates: m/M = cosθ

Tl = Tsinθ = ma

Ty = Tcosθ = mg

tan = a/g

a = gtanθ

a = gtan cos-1m/M)

(c = mgtan cos-1m/M)

Practcal 2: Turntable and Centripetal Force

Tio masses are ylaced on a turntable rotatng at a constant syeed.

(orces actng on masses:

Normal force

Weight force

Statc fricton force

Statc fricton (s= μsN) is yroviding the centriyetal force in this system.

1. What hayyens if ie move one mass closer to the centred

The mass further out iill fall oi frst

2. What hayyens ihen ie increase the syeedd

Both masses fall oi faster

. What hayyens if ie mak e one mass heavier than the otherd

They stll fall oi at the same tme

4. Hoi do ie calculate coefcient of statc fricton from this yractcald

We can rearrange ω = √μsg/r to give μs = rω2/g. (ind the malimum angular velocity you can

set the turntable to before the mass slides oi. Place the mass at a set radius.

The mass slides oi ihen (s < (c required. The malimum amount of force fricton can elert is given

by (s= μsN. Statc frictonal force on the turntable iill increase as the turntablees syeed increases,

untl (s = (c afer ihich, the mass iill slide oi.

(c = mv2/r but, v = rω

∴ (c = m rω)2/r

= mr2ω2/r

= mrω2

The yenny slides oi ihen:

(s = (c

μsN = mrω2

but, N = mg, on fat surfaces,

μsmg = mrω2

Solving for malimum angular velocity for obedect to stay in UCM:

ω2 = μsmg/mr

= μsg/r

∴ ω = √μsg/r Note: formula is indeyendent of mass hence, mass has no imyact NOT SAME AS

CR+T+CAL SPEED

(actors that infuence ihen the mass fies oi:

Radius

o Larger radius mass fies oi sooner direct) as a larger radius means that angular

velocity is higher. Higher angular velocity greater ac greater (c

(ricton

o Higher statc coefcient of fricton mass remains in UCM for longer inverse)

Syeed of turntable

o Higher syeed increasing orbital velocity) mass falls oi faster greater ac

greater (c

o can ie get your oyinion both acceyted, use formula donet eltrayolate

Mass does not infuence ihen the mass fies oi as

are ie fnding (c requiredd Because closer distance to centre of the turntable, k eeys it on the

turntable for longer but shouldnet a smaller radius require greater centriyetal forced Why is mass

irrelevant ihen mv2/rd

Non-Uniform Circular Moton

Ayyarent ieight is equal to the normal force N or (n) actng on you. Due to Neitones rd Lai ihere

each force has an equal and oyyosite reactonary force, the bigger the normal force the heavier you

feel. Using Neitones 2nd lai: (net = mac = mv2/r thus, net force is yroviding centriyetal force

Thus, at the toy of the diy you feel lighter as the normal force N or (N) on you has decreased and at

the botom you feel heavier as normal force increases.

htys://iii.youtube.com/iatchdv=b-(AfNaiZ6M htys://iii.youtube.com/iatchdv=TiOo0b-

giy+

Loop de Loop

At the botom of a diy, the normal force has to be greater than the gravitatonal force mg) as if not, you iould not be able to travel uyiards net force uy) and comylete yartal circular moton. There is an acceleraton uyiards toiards the centre of the circle – that is centriyetal acceleraton ac).Botom of the diy: N = (net + mg = mac + mg = mv2/r + mg = (c + mg (c = N – mg

At the toy of a diy, the gravitatonal force has to be greater than the normal force as the cart is heading doiniards net force doin) to comylete yartal circular moton. There is a gravitatonal acceleraton vertcally doiniards toiards the centre of the circle g).Toy of the diy: N = (net – mg = mac - mg = mv2/r – mg = (c - mg (c = N + mg

As yer Neitones 2nd lai,

(net = ma thus, in the radial directon:

(net = mv2/r

At the toy, both mg and N are actng in the same directon.

Toy: (net = mg + N = mv2/r = mg + N N = mv2/r – mg thus, you feel lighter

Botom: (net = N – mg = mv2/r = N – mg N = mv2/r + mg thus you feel heavier

Mechanical Energy

Mechanical energy = k inetc energy K) + yotental energy U)

Mechanical energy is aliays conserved unless iork is done by an elternal force. Sometmes energy

is transformed light, heat, sound.

K before + U before = K afer + U afer

Work

Work is the transfer of energy from one obedect to another or the transformaton of energy from one

form to another.

A force does iork on an obedect ihen it causes a disylacement in the directon of the force. W = (s if

force yarallel) = (scosθ force and disylacement vectors) ihere s is disylacement )m), ( is force N)

and θ is angle betieen force and disylacement

Torque

To mak e an obedect rotate a torque τ) needs to be ayylied UCM). A force acts to yrovide this turning

eiect.

A torque is due to a force actng on an obedect at a distance r) from the yivot yoint alis of rotaton).

τ = r⊥f turning yoint to end of lever) or rfsinθ ihere r is lever arm length m), f is force N) and θ is

angle betieen level arm and force ayylied

Unit is Nm, neiton metres, theta is angle betieen force and the lever

An obedect can orbit elternal alis) i.e. earth orbitng the sun or syin internal alis) i.e. earth syinning

on alis

Torque is yroyortonal to and causes angular acceleraton in rotatonal moton:

∆ω/t ∝ τ

Torque is ayylied ihenever there is a force actng tangentally to rotatonal moton:

Torque iill increase angular velocity if tangental comyonent of the force is in the same

directon as velocity

Torque iill decrease angular velocity if tangental comyonent of the force is in the opposite

directon as velocity

An obedect in rotatonal equilibrium has no net elternal torque. +t may mean that the obedect is not

rotatng or rotatng at constant angular velocity.

Moton in iravitatonal (ields

IQ: How does the force of gravity determine the moton of planets and satellites?

A gravitatonal feld is an area or region ihere an obedect iith mass elyeriences a force of atracton

toiards a larger mass. Earthes gravitatonal feld strength changes iith radius: g = 1/r2

The Earthes gravitatonal feld is given by: g = iME/rE2 ihere g is gravitatonal feld strength, i is

universal gravitatonal constant, ME is mass of the Earth, r is distance from the centre of the earth, rE

is radius of the earth.

Derivaton:

(g = mg

g =fg/m = iMm/r2 l 1/m = iM/r2 therefore, g = iM/r2 NOT ON (ORMULA SHEET

note: ihen a queston syecifes alttude, to fn radius r) you must add the radius of the earth.

Factors afectng gravitatonal feld strengta

The larger the mass of the ylanet M), the greater the gravitatonal force direct)

The larger the r, the smaller the g inverse square) decreases by a factor of 2

Acceleraton due to gravity is equal is magnitude of gravitatonal feld strength.

Neitones Lai of Universal iravitaton

Neitones Lai of Universal iravitaton allois us to calculate the amount of gravitatonal atracton

betieen tio obedects of mass. +t states that every obedect in the universe atracts another obedect iith

a force directly yroyortonal to the yroduct of their masses and inversely yroyortonal to the square

of the distance from their centres. +t is given by:

( = iMm/r2 ihere ( is gravitatonal force N), i is the universal gravitatonal constant 6.67 l 10 -11

Nm2 k g-2), M is the mass of the central obedect k g), m is the mass of orbitng obedect k g), r is radius

distance of seyaraton centre to centre, radius of orbit) m)

Predictng gravitatonal feld strengta at any point in a g feld

Orbital moton of Planets and Satellites

Kepler’s Law of Planetary Moton

Johannes Keyler student of Tycho Brahe royal astronomer to King of Denmark ) formed three

emyirical lais from years of recording and observing the traedectories of ylanets and stars.

Law of Ellipses

Each ylanet moves in an elliyse oval) iith the sun at the foci sun is closer to one side) causing,

summer and iinter. Keyler identfed the orbits of satellites as slightly elliytcal.

Law of Areas

The radius line of each ylanet sieeys out equal area in equal tme. Planets as they travel behind the

sun travel slightly faster as they are covering a longer arc length ihereas, ylanets travel sloier ihen

further aiay from the sun as they are covering a shorter arc length. This is due to the sun not being

centred. The tme to travel from Q to P = tme to travel from S to R therefore, area QOP = area ROS.

Law of Periods

Keyleres third lai ias calculated in 1619 from observatons of ylanetary moton by Tycho Brahe.

Keyler found there is a relatonshiy betieen yeriod T) of a satellitees orbit and its radius r). The

square of the yeriod T) of the ylanet is yroyortonal to the cube of their average distance r) from

the sun as distance varies due to elliytcal orbit. The lai is quantfed by:

r /T2 = iM/4π2 ihere r is orbital radius centre to centre m), T is yeriod of orbit tme for ylanet to go

around once s), i is gravitatonal constant, M is mass of central obedect k g).

Asserts that the rato r /T2 = k is the same for all ylanets. 4π2/iM is a constant for all satellites

orbitng around mass M

T2earth/r

earth is yroyortonal to T2

mars/r mars

Applicatons

The orbital moton of ylanets and artfcial satellites launched by humans, orbitng larger mass eg:

iPS satellite) can be modelled and elylained using gravitatonal felds. We can calculate star masses,

orbital velocity or orbital yeriod of these ylanets and artfcial satellites.

To ansier these questons, ie combine UCM iith Neitones Lai of Universal iravitaton.

+n orbits, gravitatonal force yrovides the centriyetal force hence:

( = iMm/r2 = mv2/r = 4π2rm/T2 = mg link betieen them

Thus,

iMm/r2 = mv2/r

iMmr/r2 = mv2

v2 = iMmr/mr2

v2 = iM/r

v = √iM/r ihich can be used to fnd centriyetal acceleraton:

ac = v2/r = iM/r2

or to calculate mass M) of stars from orbital yeriod T) and radius of ylanets orbitng a star r) as

2πr/T gives linear velocity.

Mass of central object (M): from Kepler’s Third Law in kg

r /T2 = iM/4π2, ihere M = 4π2r /iT2

Mass of orbitng object (m):

( = iMm/r2 = mv2/r, m = (cr/v2 or (cr

2/iM if you donet have orbital velocity

Orbital period (T): from Kepler’s Third Law,

r /T2 = iM/4π2

T = √4π2r /iM or 2πr/v

Orbital radius (r): from Kepler’s Third Law,

r /T2 = iM/4π2

r = ∛iMT2/4π2, ihere r = orbital radius m) = earthes radius + alttude

Orbital velocity (v):

v = 2πr/T or v = √iM/r or v = √(cr/m

Gravitatonal Potental Energy in Orbit

Potental energy is defned as the iork done by an uyiard elternal force on an obedect as it is

loiered from one yoint to another at constant syeed. +t is given by:

U = -iMm/r ihere U is yotental energy J), i is universal gravitatonal constant, M is mass of

central mass k g), m is mass of smaller mass k g), r is distance centre to centre betieen the tio

masses m)

Negatve means the gravitatonal force is atractve. +f you iant to move tio obedects further ayart

you have to do yositve iork ak a add energy by ayylying a force oyyosite to the feld. iravitatonal

yotental energy of tio masses is yroyortonal to the yroduct of the masses and inversely

yroyortonal to the seyaraton. +t is also negatve ak a atractve.

iravitatonal yotental energy is defned by the iork done in moving an obedect against the

gravitatonal feld in moving a mass from surface of earth to a height h) above. +t is given by:

U = mgh ihere m is mass k g), g is gravitatonal feld strength or acceleraton, h is height m). This is

derived from W ed) = (s N) = mgs h) height is disylacement.

Comyarison:

U = mga U = -GMm/r

Defne iork done in moving an obedectagainst the gravitatonal feld in moving a mass from surface of earth to a height h) above

The iork done by an uyiard elternal force inloiering a mass from infnity to a distance r) fromthe centre of the Earth

iithout acceleraton.

Waen is it used? Near the earthes surface h << rE

so g is constantUsed for large height changes ihen r > rE or far from Earthes surface

As r increases… U ayyroaches infnity U ayyroaches 0

Waen U = 0 At surface of the Earth +nfnite distance aiay from the centre of the Earth

Total Energy of a Planet in Its Orbit

Total energy is equivalent to mechanical energy ihich is K + U. Kinetc energy of a satellite in orbit is

given by:

K = ½mv2 = ½m l √iM/r)2 = iMm/2r

Thus, total energy is given by,

E = K + U = -iMm/r + iMm/2r = -iMm/2r NOT ON (ORMULA SHEET

Near Earta and Geostatonary Orbits

Satellites in orbit around the Earth are classifed as loi, medium or high orbit.

1. Low Orbit (180km – 2000km) alttude

Most common satellite orbit Hubble telescoye, 540k m or internatonal syace staton,

400k m, syy, military, mayying satellites).

Orbital Period T)= ayyrol. 90min but 80-120min

Whole of the Earthes surface can be quick ly covered

2. Medium Orbit (2000km – 36000km) alttude

Used by global yositoning systems iPS)

Orbital Period T) = ayyrol. hrs but -22hrs

3. Higa Orbit (36000+ km)

Used by communicatons satellites, eg: Oytus, deey syace ieather imaging etc…

A ieostatonary satellite has a yeriod T) of 24hrs iith the Earth thus, ‘statonarye as it stays

above the same yoint on Earthes surface if at equator). Used for communicatons eg: satellite

yhones, TV.

ieo-synchronous is ihen satellite syins as same rate of Earthes syin. Thus, it has the same rotatonal

yeriod but, orbit may not be yerfectly circular and may have an orbital inclinaton.

A ieostatonary satellite is a syecial case of a geo-synchronous satellite ihere the orbit is circular

and orbital inclinaton is 0.

Energy Changes that Occur ihen Satellites Moves Betieen Orbits

When an obedect moves from a high orbit to a loier orbit, it moves through an increasing i feld

strength as the gravitatonal force g or (g) on the obedect increases as it ayyroaches Earth. The

change in gravitatonal U is given by: ∆U = Ufnal – Uinital in edoules.

Waen one object moves witain tae gravitatonal feld of a second object:

Moves wita tae feld Moves against tae feld

Isolated Work is done by the feld yotental energy decreases ihile k inetc energy increases

Work is done on the feldU increases, K decrease

Open or Closed Work is done by elternal agent and by the feldU decreases, K increases

Work done by elternal agent and on the feld,U increases, K either deyends ihich does more iork )

iravitatonal U is a binding energy. To escaye from earth's gravitatonal feld, given you have mass m

you must do iork thates equal or above gravitatonal U.

Work is given by:

W = (s = (c l s = iMm/r2 l r = iMm/r

Concept of Escape Velocity

Escaye velocity is ihen a rock et has enough k inetc energy K) to escaye the Earthes gravitatonal

feld. Escaye velocity is the minimum velocity for an obedect at the surface of Earth to escaye to syace

and not be yulled back . Earthes escaye velocity is 11200 m/s MEM.

(or a satellite to escaye gravitatonal feld,

K = U at a minimum)

U = -iMm/r

½mv2 = -iMm/r

v2 = -2iM/r

Thus, minimum velocity for satellite to make it out alive is given by,

vescaye = √2iM/r NOT ON (ORMULA SHEET ihere vescaye is escaye velocity m/s), M is mass of central

body k g), i is universal gravitatonal constant, r is orbital radius centre to centre) m)

note: do not confuse escaye velocity iith orbital velocity

(actors that infuence vescaye:

Smaller radius r) higher escaye velocity needed inverse square root)

Larger central mass M) higher escaye velocity needed direct square root)

Escaye velocity +S +NDEPENDENT of mass of the launched obedect i.e. regardless of hoi heavy

the obedect is, the escaye velocity iill be the same for all obedects. Satellites are tyyically

launched from close to the equator toiards the east same directon of Earthes rotaton so it

can contribute to the k inetc energy of the rock et).

Module 7 Nature of Light

Prefx Relaton to base unit Abbreviaton

iiga 109 i

Mega 106 M

Kilo 10 K

Base unit 1

Milli 10- M

Micro 10-6 μ

Nano 10-9 n

Light is the smallest amount of energy that can be transyorted. +t has a iave yartcle duality being a

yhoton as iell as an electromagnetc iave. Visible light is betieen 400-700nm.

Light is created ihen an electron in its elcited state droys back to a loier energy state and loses

elcess energy in the form of EM radiaton.

The moving charge of an electron creates an oscillatng magnetc feld yeryendicular to an oscillatng

electric feld.

Wave and Partcle Model of Light

IQ: What evidence supports the classical wave model of light and what predictons can

be made using this model?

Newton's Corpuscular Taeory Huygen’s Wave Model

Neiton yroyosed that light ias made uy of tny yerfectly elastc partcles. Neiton concluded that travel in straight lines in all yossible directons thus, they iere yartcles not iaves as iaves yroyagate Rate at ihich they travel deyend on the medium they are in.Believed ligat must be a partcle as it travelled in a vacuum and iaves iere believed to require a mediumReflecton of light is edust lik e the rebound of a yerfectly elastc ball elylains equality of angle of incidence and angle of refecton). Refracton ias due to change in syeed of yartcles caused by net atracton of yartcles toa medium iith more mater hoiever, he thought light travelled faster in denser mediums eg: iater.When a ray is in a medium the ray moves in a straight line as Neitones 1st Lai states that the ray iill not bend if no net elternal force none since atracted equally on all sides)Light sylits due to the size of the yartcle Theory of (its), yartcles that ft betieen atoms of the medium iould refract and light that could not iould refectHe also said that diierent colours of light had diierent size yartcles thus, causing seyaraton of ihite light to occur. Light yartcles have an ambiguous, non-syherical shaye ihich allois for yolarisatonNeiton could not elylain absoryton.

Huygen yroyosed that light was a wave that propagated perpendicular to its directon of travel and has a miniscule iavelength.Huygen k nei that iaves must have a yroyagatng medium so Huygen called the medium for ligat tae ‘luminiferous aetaer’, ihich suyyosedly flls uy all syace thus, alloiing light iaves to travelHuygen's principle: Every yoint on a iavefront is a source for secondary semicircular ‘iaveletse ihich syread out in the foriard directon iith the same syeed as the iave. Thenei iavefront is the tangent to all the secondary iaves. When yart of the iavelets is block ed, the tangent is modifed.Reflecton: When the iave meets the surface at an angle, nei iavelets are created ihich form a nei iavefront that yroyagates at an angle equal to the angle of incidence

Refracton: Wavelength increases as iave enters a denser medium. The nei iavefront is shifed thus, light bends toiards the normal denser) or aiay from the normal less dense). Predicted that light travelled sloier in iater than in air.

Difracton: Waves are able to diiract, diiracton is due to iave interference. Litle diiracton is due to small iavelengths and large slits ihich elylains rectlinear yroyagatonA ylane iave is an infnite suyeryositon of syherical iaves.Light diiracted ihen going around obedects. +f light ias a iave, it iould be able to diiract. The evidence for this ias the blurred edges of a shadoi ihich iere not elylained by Neitones yartcle model but could be elylainedthrough iave interference in Huygenes model.Evidence:Poisson syot ihich is the brightest syot of a circular shadoi located at the centre of the shadoi ihen a yoint source of light is shone onto a ball or disc. This could be elylained iith iaves as the iaves diiract and then constructvely interfere at the Poisson Syot leading to a bright syot ihere there isnet any direct light source+n 1850, (oucalt also shoied that light sloied doin ihen it entered iater from air, as yredicted by Huygenes modelYounges Double Slit ElyerimentEvidence for the iave nature of light includes refecton, refracton, diiracton, interference and yolarisaton.

Wavefront: contnuous line or surface containing yoints aiected in the same iay by iave at a given

tme.

Interference: tio iaves suyerimyosed to form a resultant iave of greater, loier or same

amylitude.

Diiracton

Process by ihich a beam of light is syread out as a result of yassing through a narroi ayerture or

across an edge. +t is observed ihen iaves syend around the barrier or through an ayerture. The

most yronounced diiracton occurs ihen the size of the ayerture is close to the iavelength of the

incident iaves. Diiracton is a feature of all iaves.

Diiracton gratngs have yarallel slits gays) ihich light yasses through. As light yasses through the

gay it bends at the edges leading to destructve or constructve interference.

Single Slit Difracton

When monochromatc light light of a single iavelength/frequency) is yassed through a narroi slit,

Huygenes iavelets alloi the iave to interfere iith others as iell as turn corners thus, causing an

interference yatern on the screen.

+f one iavefront yasses through the lef of the slit and another from the right, ihen they meet, they

iill have travelled slightly diierent distances. This diierence is the yath diierence. +f iavefronts are

aligned ihen they meet, they iill constructvely interfere, if they are out of yhase by 180o they iill

destructvely interfere. This interference causes the interference yatern.

Most light energy is concentrated on central malima iave travels equal distance from both sides of

the slit).

A diiracton gratng is ihen light yasses through a number of slits. They're used ihen light of

diierent iavelengths needs to be seyarated at a high resoluton. Light iaves emerging from the

gays iill interfere iith light iaves from adedacent gays to create an interference yatern. They are

used in syectrograyhs.

Conditon for destructve interference for single slit:

dsinθ = mλ ihere d is slit iidth m) for single slit diiracton, θ is angle of diiracton, m is order of

interference, λ is iavelength m)

Single slit iavelength:

λ = ½yd/mL ihere y is node to node 1/2y is central bright to midline of dark ), d is slit iidth m), m is

order of interference, L is distance from slit to screen m)

1801 Young's Double Slit Elyeriment

+n 1801, Thomas Young designed his double slit elyeriment on the basis that:

+f light ias a iave then ihen tio rays of light meet there must be interference

The interference iould either be constructve or destructve

He understood beat frequencies yroduced from soundiave interference and he ianted to

test ihether light iould elhibit similar behaviour

(or interference to be detected, Young concluded that the tio sources must:

- Be coherent frequency and iaveform are identcal)

- Maintain constant yhase relatonshiy

- Have the same frequency iaves

- Have ayyrolimately the same amylitude

Metaod:

1. Sunlight ias frst shone through a single slit iith a red flter to create a coherent light

source monochromatc and coherent)

2. The light ias then yroedected onto a detecton screen through tio miniscule slits ihich

yroduced an interference yatern of bright and dark fringes on the screen

. Slits of diierent sizes and distances ayart iere then tested

4. Young ias able to calculate the iavelength associated iith light as iell as yrovide

convincing evidence for Huygen's iave model

Using: y = mλL/d for small angles L >> d ihere y is antnode seyaraton on screen middle of

one bright syot to nelt bright syot), λ is iavelength, L is distance from slit to screen, d is slit

iidth, m is order of interference central malima is 1, one to the right is 2, lef is -2…).

Or using:

y = m+1/2)λL/d for small angles L >> d ihere y is node seyaraton on screen dark to dark ),

m is order of interference, λ is iavelength m), L is distance betieen screen and slit m) and

d is slit seyaraton m)

Findings: This resulted in the formaton of an interference fringe consistng of clear light and dark

sectons on an observaton screen. The only iay this could hayyen ias if light ias a iave because

otheriise adding more light yartcles to an area should not yroduce a secton of no light.

The negatve and yositve sectons of the interference yatern iere due to constructve bright light,

in yhase) and destructve no light, 180 degrees out of yhase) interference occurring.

He ias able to calculate the iavelength of light by using distances betieen 2 areas of constructve

interference and 2 areas of destructve interference as y.

Pata diference: Diierence in distance travelled by tio iaves to a yoint on the screen

Constructve interference occurs ihen the yath diierence is 0 or ihole number of iavelengths.

Conditon for constructve interference for double slit:

dsinθ = mλ ihere d is slit seyaraton m) for double slit diiracton, θ is angle at ihich constructve

interference occurs, m is order of interference, λ is iavelength m)

dsinθ = m+ 1/2)λ ihere d is slit seyaraton m) for double slit diiracton, θ is angle at ihich

destructve interference occurs, m is order of interference, λ is iavelength m)

θ is angles at ihich constructve/destructve interference occurs deyends ihat formula)

Double slit wavelengta:

λ = yd/mL ihere y is central malima to nearest antnode, d is slit iidth m), m is order of

interference, L is distance from slit to screen m)

Diiracton gratngs contain a large number of yarallel, closely syaced slits or grooves. They yroduce

interference malima at angles θ given by dsinθ = mλ ihere distance betieen slits is d, angle to a

bright fringe of a yartcular colour is θ, m is order of interference, λ is iavelength

Path diierence: mλ

Relatonsaips:

The central intensity is yroyortonal to the square of the number of sources. direct square)

The smaller the iavelength RELAT+VE to the slit, the less diiracton direct)

The greater the iavelength RELAT+VE to the slit, the greater the diiracton direct)

(ringe seyaraton is D+RECTLY yroyortonal to iavelength/frequency of radiaton forming it

direct)

Width of the diiracton yatern is +NVERSELY yroyortonal to slit iidth inverse)

With double slit interference ie stll have a diiracton enveloye, inside that there are the

interference fringes.

Syreading out of the diiracton enveloye is determined by iidth of the slit ihereas fringe

seyaraton is determined by syace betieen tio slits.

Decreasing slit seyaraton increases fringe seyaraton inverse)

+ncreasing iidth of the slit, central malimum narrois inverse)

+ncreasing L distance from screen to slit), increases fringe seyaraton direct)

Decreasing d, increases fringe seyaraton inverse)

Polarisaton

Polarisaton occurs ihen a transverse iave is alloied to move only in one directon.

Light yroduced by a light globe or the sun comes out as iaves in all ylanes. A light iave that is

vibratng in more than one ylane is referred to as unyolarised light. Such light iaves are created by

electric charges that vibrate in a variety of directons, thus creatng an electromagnetc iave that

vibrates in a variety of directons.

Polarised light iaves are light iaves in ihich the vibratons occur in a single ylane. The yrocess of

transforming unyolarised light into yolarised light is k noin as yolarisaton.

THIS FORMULA FOR THE SECOND POLARISER OF A TWO POLARISER QUESTION, to fnd intensity

caange of a single polariser it is simply ½ original intensity

Maluse Lai:

+ = +0 cos2θ ihere +0 is the intensity of the yolarised iave before yassing through the flter Wm), + is

intensity of transmited iave Wm) and θ is angle betieen the tio yolarisaton ales o) negatve to

the lef, yositve to the right).

The frst yolarizing flter is called the yolarizer, the second yolarizing flter is called the analyser.

(actors that infuence intensity of transmited iave +):

Analyser angle

o Sinusoidal relatonshiy ihen intensity of + is yloted against y alis) analyser angle

relatve to yolariser angle l alis)

When analyser is at angle of 0o relatve to the yolariseres yolarising alis,

intensity is at a MAX+MUM of 0.5+0

+ntensity ayyroaches zero as angle increases inverse)

The same angle either yositve or negatve, have the same imyact on

intensity of transmited iave +0)

+/+0 vs cos2θ gives a yositve linear grayh.

Summary of Investgaton:

+V: Angle betieen yolariser and analyser angle θ)

DV: intensity of transmited light +)

CV: angle of yolariser, intensity of source +0), distance betieen yhotodetector and analyser,

distance betieen yolariser and analyser

Aim: Reafrm Maluses Lai

Method:

1. Clamy one yolarising flter to the retort stand by ataching the arm of the clamy iith the

boss head.

2. Adedust the yolarising flter so that the yolarising alis is comyletely vertcal using a yrotractor

and aligning iith the 90o line.

. Clamy the second yolarising flter to the second retort stand around 15cm aiay from the

frst retort stand. Adedust the flter so that the yolarising alis is yeryendicular to the yolarising

alis of the frst yolaroid flter, aligned iith 0o on the yrotractor.

4. Connect the lamy to a yoier source and ylace 5cm in front of the frst yolarising flter.

5. Connect the yhoto detector and ylace 5cm behind the second yolaroid flter analyser)

6. Adedust so that the heights of the lamy, yolariser, analyser and yhotodetector are in line iith

each other.

7. Turn on the lamy and record intensity reading on the yhotodetector.

8. Carefully adedust the angle of the analyser to 10o, measured using the yrotractor and record

reading on the yhotodetector.

9. Reyeat from angles 10-90o in the clock iise directon and 10-90o in ant-clock iise directon.

10. Record results, indicatng diierent directon iith – for ant-clock iise and + for clock iise.

Equiyment:

Protractor

2 yolarising flms

Unyolarised source of light lamy)

Photo detector

2 clamys

2 retort stands

2 boss heads

(orms of yolarisaton:

Polarisaton by polaroid flter

A yolarising flter only transmits comyonents of the iave in a yartcular directon and absorbs the

rest. A yractcal ayylicaton is yolarising sunglasses, ihich absorb light in a yartcular ylane, reducing

glare. The chemical comyositon of the yolaroid flter allois one ylane of iaves to yass through and

the other ylane of iaves yarallel to the molecular alignment of the flter to be absorbed by the

flter. When unyolarised light is transmited through a yolaroid flter, it emerges iith one-aalf the

intensity and iith vibratons in a single ylane.

The yolarisaton alis is yeryendicular to molecule alignment and eltends across the length of the

flter. +t only allois vibratons of the electromagnetc iave that are yarallel to the alis to yass

through. Any vibratons that are yeryendicular to the yolarisaton alis are block ed by the flter. The

flter does not distort the shaye or dimensions of the obedect it yroduces a dimmer image of the

obedect since one-half of the light is block ed.

The angle betieen the directon of yolarisaton and the alis of a flter is θ.

+f the electric feld has an amylitude E, then the transmited yart of the iave has an amylitude

Ecosθ. Since the intensity of a iave is yroyortonal to its amylitude squared, the intensity of the

transmited iave is related to the incident iave by Maluses Lai:

+ α E2

E = E0cosθ

E2 = E02cos2θ

+ = +0cos2θ

Polarisaton by reflecton

Unyolarised light can also undergo yolarisaton by refecton oi of non-metallic surfaces. Eltent of

yolarisaton is deyendent uyon angle of lightes ayyroach and material of surface. The refected ray is

fully yolarised horizontally vibratng in a ylane that is yarallel to the surface of the material) at

Breisteres angle angle of ihich refected light is fully yolarised, refracted and refected beam are

yeryendicular, unique to each medium) as ihen the incident light crosses the interface, the light is

absorbed temyorarily by atoms in the second medium. Electrons in these atoms oscillate back and

forth in the directon of the electric feld vectors in the refracted ray, yeryendicular to the directon

the refracted light is traveling. The light is re-emited by the atoms to form both the refected and

refracted rays. The electric feld vectors in the light match the directon the electrons iere

oscillatng, and they must be yeryendicular to the directon of yroyagaton of the iave. When light

comes in at the Breister angle the refected iave has no electric feld vectors yarallel to the

refracted ray, because the electrons do not oscillate along that directon. The refected iave also

has no electric feld vectors yarallel to the refected ray, because that's the directon of yroyagaton

of the iave. The only directon yossible is yeryendicular to the ylane of the yicture, so the refected

ray is linearly yolarised

(ormula for Breisteres Angle:

n = sin θi)/sin θr) = sin θi)/sin θ90-i) = tan θi) ihere n is the refractve indel of the medium from ihich

the light is refected, θi is the angle of incidence, and θr is the angle of refracton.

+f the angle betieen the refected ray and refracted ray is 90° then the refected light is comyletely

yolarised in one ylane.

Polarisaton by refracton

Polarisaton can also occur by the refracton of light. Refracton occurs ihen a beam of light yasses

from one material into another material. At the surface of the tio materials, the yath of the beam

changes its directon. The light transmited into the medium is yartally yolarised as it has lost the

refected light that is yolarised by the refectng surface.

if an obedect is vieied by look ing through an +celand Syar crystal, tio images iill be seen. The tio

images are the result of the double refracton of light. Both refracted light beams are yolarised - one

in a directon yarallel to the surface and the other in a directon yeryendicular to the surface. Since

these tio refracted rays are yolarised iith a yeryendicular orientaton, a yolarizing flter can be

used to comyletely block one of the images.

Polarisaton tarouga scatering

Polarisaton also occurs ihen light is scatered ihile traveling through a medium. Since light iaves

are electromagnetc EM) iaves transverse iaves) they iill vibrate the electrons of air

molecules yeryendicular to the directon in ihich they are traveling. Vibratng electrons then

yroduce EM radiaton that is yolarised yeryendicular to the directon of the ray. The light yarallel to

the original ray has no yolarisaton. The light yeryendicular to the original ray is comyletely

yolarised. +n all other directons, the light scatered by air iill be yartally yolarised. Polarisaton by

scatering is observed as light yasses through our atmosyhere. The scatered light ofen yroduces a

glare in the sk ies. See gif.

The fact that light can be yolarised is an imyortant yiece of evidence for the iave nature of light, in

yartcular that light is a transverse iave as light can be yolarised and only transverse iaves can be

yolarised.

IQ: What is light?

EMR

The iavefront of electromagnetc iaves emited from a yoint source such as a light bulb) is a

syhere. EM iaves carry energy E), momentum y) and angular momentum L) aiay from their

source yartcle and can imyart those quanttes to mater iith ihich they interact

The electromagnetc syectrum is sylit into ionising and non-ionising radiaton. +onising includes:

gamma rays, l-rays, ultraviolet and means that these iaves have enough energy to break chemical

bonds and striy atoms of electrons. Non-ionising includes: visible light, infrared, microiaves and

radio iaves and means that these iaves cannot break chemical bonds or ionise atoms hence, they

are not dangerous. Waves are listed in order of smallest iavelength to largest iavelengths.

All obedects ihose temyerature is above 0K emit EMR. The elact tyye deyends on the energy of the

obedect and not on the characteristcs of the material.

When an obedect starts to heat uy, it may radiate heat infrared) but may not emit visible light. As the

obedect is heated further, the obedect iill begin to gloi red, releasing red as visible light. Aferiards,

orange, yelloi, ihite and then blue as the temyerature increases. The higher the temyerature, the

higher the frequency. Therefore, the EMR emited is due to the obedect's temyerature. LED light

emitting diode) and fuorescent light oyerate iith a diierent method.

+n quantum mechanics, EMR consists of yhotons ihich are miniscule elastc yartcles that elhibit

iave-yartcle duality and have energy quantsed as yer E = hf.

Malielles Contributon

Maliell iork ed iith 4 lais to yroduce a unifed theory of classical electromagnetsm. These are:

iauss's Lai of Electrical (lul yoint charges radiate an electric feld outiards as if there is a net

charge inside a iaussian surface surface that smoothly encloses charge), there must be charge

leaving it

iausses Lai of Magnetc (lul B feld lines are aliays looyed thus, there are no magnetc

monoyoles

(araday's Lai of Electromagnetc +nducton a changing magnetc feld generates a changing

electric feld

Amyere's Circuital Lai a changing electric feld generates a changing magnetc feld yeryendicular

to the ylane of the electric feld using the disylacement current). +nvolves μ0 and ε0 ihich can be

measured in laboratory.

Predicton of EM waves:

Maliell yredicted that EM iaves are made uy of tio mutually simultaneously) yroyagatng

electric and magnetc felds at right-angles to each other ihich are self-yroyagatng and eltend into

syace vacuum). He also yredicted that EMR ias light and also that EMR had a large range of

frequencies beyond the visible syectrum.

Explanaton: A yroyagatng electric feld generates a yroyagatng magnetc feld as changing electric

ful induces a magnetc feld. This generated magnetc feld in turn generates an area of changing

magnetc ful see diagram) as the closed looy formed by the resyectve yoints of the transverse

iave form an area ihere a changing magnetc ful occurs thus, inducing a changing electric feld.

This cycle allois EM iaves to travel in a vacuum iithout an elternal yroyagatng force.

Producton of EMR: Every accelerated charge velocity needs to change either by change in directon

or syeed) radiates EMR. A moving electron yroduces a magnetc feld, but this magnetc feld is

constant because the electrones moton has a constant velocity. +n order for an electron to radiate

Electromagnetc EM) radiaton, it needs to accelerate as changing magnetc felds yroduce changing

electric felds, causing self-yroyagaton. A charged yartcle oscillatng about an equilibrium yositon

is an acceleratng charged yartcle. +f its frequency of oscillaton is f, then it yroduces an

electromagnetc iave iith frequency f. The iavelength λ of this iave is given by λ = c/f.

You set uy a broadcastng antenna iith an AC yoier source ihich yroduces EMR ihich can be

received by a receiving antenna at some distance aiay tuned to receive the frequency of EMR

emited. hoi radios iork )

Maxwell found taat EM waves travelled at tae speed of ligat. He theorised that the electrical and

magnetc constants should be related as electricity and magnetsm are related. Dividing the electric

constant by the magnetc constant, he found that the units iere m2/s2 ihich ias a square of the

units of velocity. Square rootng his ansier 1/√μ0ε0), he found that it ias very close to the syeed of

light. This yrovided evidence that light ias EMR.

Heinrica Hertz’s Evidence for Maxwell:

Hertz measured the iavelength and frequency of light by doubling the measurement of consecutve

bright syark yoints of his generated standing iave. Hertz ias also the frst yerson to observe the

yhotoelectric eiect.

He surmised that the syark yroduced in the broadcastng antenna iould induce a small syark in the

receiving antennae as the EMR reaches it. This ias ihat had occurred thus, he concluded that there

ias an EM iave betieen the tio antennae.

He found that EM iaves are able to be refected by ylacing a refectve sheet betieen the tio

antennae.

And refracted as ihen he ylaced yitchblende betieen the tio receivers, he had to move the

receiver to observe the syark .

He lined uy the refectve sheet iith the receivers so that a standing iave ias noi yroduced:

And he moved the receiver to observe ihen large syark s occurred. He notced that large syark s

occurred at the antnodes.

By measuring distance betieen successive bright syark s ihich ias equivalent to λ/2, he could

double it and fnd the full iavelength. The frequency ias k noin thus, he could fnd velocity of the

iave using v = fλ ihich v = c, validatng Malielles yredictons.

How did ae discover tae paotoelectric efect?

He ylaced his ‘receivere coil in a dark bol ihich caused the syark induced in the receiver to diminish

considerably. Bafed, he ylaced a yane of glass in front of the receiver, ihich caused the syark 's

intensity to diminish more but, iith a quartz screen the syark remained close to its intensity in air.

This ias because the glass screen block ed some of the unseen UV rays of EM radiaton that

contributed to the syark E = hf).

Measuring Velocity of Light

Historical

Galileo

Whend 16 8

Princiyled +f a tme lag could be found it shois that the syeed of light is indeed fnite. +f the distance

betieen the tio yeoyle ias recorded and the tme lag found then one could calculate the syeed of

light using v = s/t.

Methodd

1. Tio yeoyle stood a k noin distance from each other, holding a covered lamy2. One yerson iould uncover their lamy . Once the other yerson sai the light of the uncovered lamy, they iould also uncover their

lamy.4. The tme lag betieen the frst yerson uncovering their lamy and the second yerson

uncovering their lamy iould be t used in v =s/t and ias measured using ialileoes yulse5. Steys 1-4 iere reyeated iith yrogressively greater distances untl the tio yeoyle needed

telescoyes to see each other

6. Reyeated each distance to minimise imyact of reacton tme on result random error)

Valued +nconclusive, no value ias found as there ias no yerceytble tme lag. ialileo only concluded

that the syeed of light ias ‘+f not instantaneous, it is eltraordinarily rayide and deduced that it ias

10l faster than the syeed of sound.

Pros vs consd Method ias not valid in determining the syeed of light as the syeed of light ias too

rayid to have a yerceytble tme lag.

(igure 5 red is NO syark , blue is BR+iHT syark

λ/2

Lack of reliable scientfc equiyment such as the lack of a yrecise tming device to ayyrolimate tme

lag.

Variables such as the yersones eyesight iere not controlled. This iould have large imyacts ihen

distances increased and telescoyes had to be used.

Roemer

Whend 1676

Princiyled Due to the diierence betieen the tme ihen ecliyses iould occur ihich are deyendent

on the yositon of Earth. He concluded that the syeed of light ias fnite, as he deduced that the

ecliyse ias delayed because light had to travel a longer distance hence, syeed of light ias not

instantaneous.

Methodd Romer studied the movement of +o Juyiteres moon) around Juyiter by recording the tmes

of ecliyses over the course of many years. Hoiever, contrary to his elyectaton that the interval

betieen subsequent ecliyses iould remain constant, he found that the tme interval varied in

length deyending on the distance betieen Juyiter and Earth. When Earth ias closest to Juyiter

oyyositon) the ecliyse iould be 11 minutes earlier than yredicted ihereas ihen the Earth ias

farthest from Juyiter coneduncton) it iould ecliyse 11 minutes later than yredicted tme. Romer

concluded that this ias due to the fnite syeed of light.

The syeed of light could then be found by measuring the tme delay betieen yositon of coneduncton

and oyyositon and then diving Earthes diameter by it v = s/t). Roemer estmated that light required

22min to cross the diameter of Earth.

Valued 200,000 k m/s or 210,824 k m/s ayyrol. 0% error)

Pros vs consd

Provided the frst quanttatve measurement of the syeed of light and disyroved the theory that it

ias instantaneous regardless of distance.

Hoiever, due to lack of k noiledge of the Earthes diameter of orbit and inaccuracy of tme delay

measurement due to equiyment constraints, the value is merely an ayyrolimaton and has a

yercentage error of around 0%.

Fizeau

Whend 1849

Princiyled Syeed of light is equal to tiice the distance betieen the source and the mirror used to

refect the light back that is the distance light travels in total) divided by the tme it tak es to

comylete that distance v= s/t).

Methodd

1. Light source ias shone through a semi-refectve mirror, this ias done to guide the

refected beam of light back to his eye thus, reducing imyact of human reacton tme

2. Using a syinning cog iith 720 slits, the cog ias syun at a syecifc frequency so that the

beam of light iould travel through one slit uyon ayyroaching a second mirror set 86 0m

from the frst mirror and the refected beam iould travel back through the adedacent slit

uyon returning.

. Using the number of cog slits and the frequency of the coges syinning, (izeau could calculate

tme tak en for one slit to shif so that the adedacent slit iould tak e its ylace. if frequency ias

5 Hz, he iould fnd tme for 1 cog to siitch to the nelt by frst calculatng tme for 1

revoluton using T = 1/f = 1/5 s and then dividing 1/5 by 720, 1/ 600 s) Knoiing the angular

velocity in revolutons yer second rys) and number of teeth, he could fnd tme tak en for

one gay to yass using c = 2dnv ihere d is distance to mirror, n is number of teeth, v is

iheeles rys or 2d/[ 1/v)/n]

4. The syeed of light ias then found by dividing the total distance travelled by the light, ihich

ias double the distance from the light source to the mirror by this tme.

Valued 1 , 00 k m/s 4% error)

Pros vs consd

Accuracy ias limited by (izeaues use of technology ihich accounted for a 4% error as iell as the

diminished source of light over large distances. Hoiever, this method ias much more accessible as

the elyeriment could be conducted in a laboratory environment terrestrial) alloiing for reyeat

trials ihich helyed increase accuracy of the syeed.

Foucault

Whend 1862

Princiyled The tme of fight of the beam of light imylies a slight rotaton of the syinning mirror in the

tme the light took to travel to the statonary mirror and back . This rotaton iill defect the returning

beam at an angle that deviates from the original yathes angle. Knoiing the frequency of the mirrores

rotaton, the equivalent tme of that angle could be calculated and thus, the syeed of light as the

travelling distance is k noin.

Methodd (oucault modifed (izeaues elyeriment by reylacing the rotatng cog iith a syinning mirror

iith a vertcal alis of rotaton.

The aim is to send the beam of light bouncing from the rotatng mirror, to the statonary mirror and

back to the rotatng mirror. The total travelled distance iould be double the distance betieen

rotatng and statonary mirror.

As v = s/t,

t = s/v, v in this case is the syeed of light c) and s is double the distance betieen the tio mirrors

2d)

t = 2d/c

let the rotatng mirror have an angular velocity of ω radians yer second

thus, the angle it moves though in the tme for light to travel and be refected back is:

θ = ωt

sub in t = 2d/c

θ = 2ωd/c

rearranging,

c = 2ωd/θ = ∆θ/∆t l 2d/θ

Valued 299,796 k m/s

Pros vs consd (oucault imyroved uyon (izeau terrestrial method through reylacing the cog and half-

silvered mirror iith one rotatng mirror, this increased the yrecision and accuracy of his results as

the angle ias measured rather than distances betieen cogs and reacton tme diminished as an

infuencing factor. The resultng value had only 0.6% error and this does not account for the fact that

(oucault measured the syeed of light in air rather than a vacuum so his margin of error may actually

be smaller.

Michelson

Whend 1879

Princiyled +f ie k noi the distance something travels and tme tak en to travel the distance, ie can

fnd its syeed.

Methodd Michelson frst chose tio distant yoints, 5k m ayart. He then installed the folloiing:

On one of the mountains he installed a regular octagonal rotatng disk of ihich the frequency of

rotatons can be measured and is constant. On each of the outiard facing fat faces of the octagon

he installed fat mirrors.

On the other mountain he installed a large concave mirror facing back to the mountain iith the

rotatng disk . At oyyosite the centre of this concave mirror ias a fat mirror facing the concave

mirror ihich alloied the beam of light to travel back to one of the fat faces of the octagonal

rotatng disk .

A light source ias shone onto one of the octagones faces so that it iould travel to the concave

mirror and back to another octagonal face as seen above, this occurred ihen the disk ias

statonary. Michelson then sloily increased the RPS of the rotatng disk untl the light ias observed

iithout interruyton 528rys) ihich is ihen the disk turns ⅛ in the tme it tak es for the light to

travel to the oyyosing mirror and back . +f the disk ias syun any sloier or faster no light iould be

able to be seen by the observer.

Elamyle calculatons:

Light travelled a distance of 2 l 5 k m = 70 k m = 7000m

The disk comyletes one full revoluton in 1/528 second

The light travels 70k m ihen the disk mak es ⅛ of a turn found by testng at ihat rotaton iill the

light directly return to the observer.

Total tme tak en = ⅛ l 1/528 = 1/4224 s

v = d/t, therefore syeed of light = 70000 l 4224 m/s = 295680000 m/s

CALCULAT+ONS ARE EXAMPLES ONL, RESULTS ARE NOT WHAT M+CHELSON iOT

Valued 299,774 k m/s

Pros vs consd His value ias very close to the acceyted value of today iith only 0.001% error from

the acceyted value. The terrestrial nature of his elyeriment alloied for multyle trials to be

conducted. The simyle nature of the calculatons ensured that calculatons had a loi chance of

error.

Contemporary

Michelson-Morley aka Laser Interferometry

Whend 1887 frst designed, used in 1972 by NBS

Princiyled V = frequency l iavelength, ias also used to determine yresence of luminiferous aether

null result)

Methodd

1. A beam of light ias shone from a laser iith a k noin frequency

2. This beam of light ias yassed through a half-silvered mirror ihich sylits the beam.

. Tio fat mirrors are ylaced ihere the sylit beams iill land.

4. These mirrors refect the sylit beams back to the half-silvered mirror ihere they noi both

travel the same yath to the detector.

5. As they are iaves travelling the same yath, interference iill occur.

6. +nterference can either be constructve ihich iould result in double intensity or destructve

ihich iould result in zero intensity.

7. To fnd the iavelength of the laser beam, the distance that one of the mirrors had to be

moved in order to achieve yerfectly constructve interference ias measured and the

distance one of the mirrors had to be moved in order to achieve yerfectly destructve

interference ias measured.

8. The diierence betieen these tio yoints is equivalent to ¼ of a iavelength thus, the

iavelength could be found by 4 l distance betieen the tio yoints.

Valued 299792.458 k m/s .5 l 10-9 relatve uncertainty)

Cavity Resonance

+nvolves indeyendently measuring the frequency f and iavelength λ of an electromagnetc iave in

vacuum. The value of c can then be found by using the relaton c = fλ. One oyton is to measure the

resonance frequency of a cavity resonator. +f the dimensions of the resonance cavity are also k noin,

these can be used to determine the iavelength of the iave. An elamyle iould be using a

microiave, if the turntable is removed, it iill cook the fastest at the antnodes the yoints at ihich

the iave amylitude is the greatest), ihere it iill begin to melt. The distance betieen tio such

syots is half the iavelength of the microiaves by measuring this distance and multylying the

iavelength by the microiave frequency, the value of c can be calculated

Speed of Ligat tarouga Water

(oucault – Syeed of Light Through Water

Metaod: He shined a light source on the rotatng mirror. The beam ient uy through a tube and met

the fled mirror above the tube. The fled mirror refected the beam back doin onto the rotatng

mirror again ihich by noi had turned a litle further), the light came back a litle beloi the source

it originated from ihere it says ‘aire in the fgure).

(oucault then reyeated his elyeriment, but flled the tube noi iith iater. +f the syeed of light is

faster in iater than it ias in the air-flled tube, the light iould return faster to the rotatng mirror

than before ihich iould have rotated less) and the refected beam iould come out above the syot

ihere the beam through air came out.

Hoiever, the elyeriment shoied the refected beam through iater came out beloi the syot

ihere the beam through air came out. This formed irrefutable evidence that light travelled sloier in

iater than in air hence, disyroving Neitones Coryuscular theory.

Speed of Ligat’s Relaton to Distance and Time

The syeed of light is no longer neily measured. +t is used to defne the length of a metre, ihich is

defned as distance light travels in a vacuum in 1/299,792,458th of a second. c is also the uyyer limit

of velocity for all conventonal mass and informaton, ie can ayyroach c but never reach it. C also

interrelates syace and tme in E = mc2. The tme diierence betieen c and the syeed v at ihich light

travels in a material is called the refractve indel n).

Syectroscoyy

Syectroscoyy +s a study of hoi EMR interacts iith mater. The syectra yroduced by certain

elements is analysed by measuring iavelength/frequency of the iaves ihich are seen as colour. +t

is used in astronomy.

Absorpton Spectra

Absoryton syectrum is yroduced through ylacing a light source behind a cool gas the samyle). The

cool gas causes certain iavelengths, distnctve to the elements contained in the gas, to be absorbed

forming black lines on a contnuous syectrum.

Emission Spectra

When elements are elcited through heatng or electricity, the electrons of the atoms absorb energy

and move to high energy levels. When they return to a grounded state, this energy is emited in the

form of electromagnetc radiaton ihich is detected as coloured lines on a black syectrum. The

colours yroduced by the element are distnctve and aid the determinaton of chemical comyositon.

The yrocesses to yroduce either syectrums diier in that the absoryton syectrum yasses the

gaseous elements through a cold gas cloud that is yositoned in front of a light source yroducing a

contnuous syectrum ihereas to yroduce an emission syectrum the light itself is yroduced by the

element through elcitng its atoms.

Syectroscoyed A syectroscoye combines a diiracton gratng iith a vieiing telescoye, alloiing a

syectrum to be observed. A syectrometer is the same as a syectroscoye but, iith an added

iavelength scale. The full range of electromagnetc radiaton is used ihen studying the universe.

Electromagnetc radiaton is emited by all obedects above absolute 0 ihich is 0K.

+nvestgaton:

Uses of Syectroscoyy

Surface Temperature

Using the measured malimum iavelength of radiaton emited by the star iith Wienes Lai λmal =

b/T), ie can fnd the surface temyerature of the star. Or simyly by look ing at the colour of the star

ie can ayyrolimate its temyerature, ihite blue yelloi orange red

Rotatonal and Translatonal Velocity

The relatve velocity of a star can be measured by blueshif: star ayyroaching observer or redshif:

star moving aiay from observer. This is due to the Doyyler eiect ihich aiects all iaves. The

Doyyler eiect occurs ihen there is relatve movement betieen the iave and observer ihich

causes an ayyarent change in frequency and iavelength. +f the iave ayyroaches the observer, the

ayyarent frequency increases and iavelength decreases thus, causing blue shif. +f the iave is

receding from the observer, the ayyarent iavelength increases and the frequency decreases

causing red shif. The red shif is shoin by the shifing of emission syectra lines toiards the lef side

ihereas blue shif shifs lines to the right side. The amount of redshif reveals the syeed of a star's

movement. By fnding the amount of blue and red shif on either side of a star ie can fnd rotatonal

velocity.

Density

Large suyergiant stars have the loiest densites toy of HP diagram), main sequence stars have

higher densites. middle of HP diagram). Astroyhysicists can calculate the:

Surface temyerature of a star

Total energy given oi by the star total light emited by star or absolute magnitude)

The mass of the star can be estmated using the closeness of syectral lines, surface temyerature and

absolute magnitude of the star ihich locates them on the HR diagram and allois distance from

observer to be calculated + yroyortonal to 1/d2). The estmated mass can then be used to

ayyrolimate the volume and radius of the star. Assuming syherical, V = 4/ πr and density can be

found using m/v. Loier density, giant stars yroduce fner absoryton lines ihile higher density,

smaller stars yroduce fuzzier ones due to more free movement of atoms and ions that are absorbing

the radiaton and loier surface gravity.

Caemical compositon

The measurement of a star's syectra indicates chemical comyositon through analysis of the

iavelengths coloured bands). The 92 chemical elements have their oin characteristc

emission/absoryton lines eg: Hydrogen i/ 4 iavelengths that it emits/absorbs. +f these 4

iavelengths are yresent in a star's syectrum, Hydrogen is yresent in its chemical comyositon as

yart of comyound or gas. When the sun's syectrum ias analysed in 1868, some bands observed did

not ft any earthen element. +t ias believed this element ias sun elclusive = helium. Most stars

have similar solar syectrums, any small diierences indicate imyortant info about the star. Our sun is

71% hydrogen, 27% helium and <2% other. over 65 elements detected in our sun. Toy 10 elements

of our sun's comyositon are Olygen 0.97%, carbon 0.4%, nitrogen 0.1%, silicon 0.1%, mg 0.08%,

neon 0.06%, (e 0.014%, Sulfur 0.04%. Other stars and nebulae have ayyrol. 90% hydrogen, 10%

helium and traces of other.

IQ: What evidence supports the partcle model of light and what are the implicatons

of this evidence for the development of the quantum model of light?

Quantum Model of Light

Blackbodies

Black bodies are an ideal surface ihich comyletely absorbs and emits all iavelengths of EMR. +t is a

theoretcal conceyt ihich can be ayyrolimated by a cavity that has its interior ialls black ened iith

a small hole in one side to ylace a temyerature yrobe in oven/ furnace). as radiaton falls on the

hole from the outside, it iill yass through. Afer yassing, radiaton is absorbed by the interior

surface and ihen emited escayes through hole), the EMR emited depends only on tae

temperature of tae cavity and is not afected by tae size of tae cavity nor by tae materials tae

cavity is made from.

The EMR emited by a black body at a constant temyerature is called black body radiaton.

The black body is an ideal obedect, not a real one and ayyrolimatons are used in yhysics. The sun is

close to a yerfect black body as black bodies are yerfect emiters as iell as absorbers because they

absorb the iavelengths that they also emit. At higher temyeratures the larger intensity of shorter

iavelengths changes the colour of the black body from red to orange, yelloi, ihite and blue as

temyerature increases.

The black body model ias founded on the black body and is used to calculate the temyerature of

distant obedects.

Tae Blackbody Spectrum

As temyerature increases, the yeak is higher on the intensity grayh, shifs lef and iavelength

decreases.

Note: mK is metre Kelvin, not milli Kelvin

+nconsistency: Wien's disylacement lai ias a successful model since it yredicted the yositon of the

yeak iavelength. Hoiever, there iere tio yroblems: 1. there ias no theory elylaining the curve

shaye of the intensity vs iavelength. 2. Wien's lai ias based on an ideal black body. Could this

theoretcal model reyresent the surface of a stard

Classical yhysics yredicted black line) that intensity iould increase infnitely as iavelength

decreased into infnity hoiever, ihen elyeriments iere done, intensity diyyed ihen it reached the

UV syectrum desyite a shorter iavelength, resultng in a curve. This could not be elylained using

classical yhysics and a nei theory ias required to solve this yroblem of 'the ultraviolet catastroyhe.'

As temyerature increases, total energy should increase. Shorter iavelengths should ayyroach

infnity.

(eature Classical Elyerimental Result

Behaviour at long iavelengths iradual decrease in syectral radiance/energy

iradual decrease in syectral radiance/energy

Peak iavelength iradual increase in yoier, no yeak

Peak iavelength deyends on temyerature according to Weines disylacement lai

Behaviour at short iavelengths

Poier ayyroaches infnity, shary increase

Poier emited is at 0 at short iavelengths

+n 1900, Planck began the era of quantum mechanics, a nei branch of yhysics. His theory matched

the elyerimental results iith his formula

He yroyosed that the vibratonal energy of atoms in a black body ias emited or absorbed in discrete

yack ets, or quanta. Rather than a contnuous release of energy, at the yeak temyerature, a syecifc

quanta escayes iith a certain amount of energy multyle of the Planck energy) E = nhf). Einstein

theorised that light ias also quantsed in the same iay, calling the ‘yack etse yhotons and using it to

elylain the yhotoelectric eiect E = hf)

As heat inside increased, at each temyerature a nei yack et of energy is released.

(ormulas:

E = hf, ihere h is the Planck constant 6.626 l 10^- 4) and f is frequency of EMR in Hz, E is energy of

a quantum of light J or eV)

E = hc/λ, ihere c is the syeed of light l108), λ is iavelength, h is the Planck constant 6.626 l 10- 4)

f = c/λ, ihere c is the syeed of light l108), f is frequency Hz) and λ is iavelength m)

y = h/λ ihere y is momentum Nm), h is Planck es constant, λ is iavelength m)

KEmal = hf – iork functon)

Wienes Lai: λmal = b/T, ihere b is Wienes disylacement constant, T is surface temyerature

Paotoelectric Efect, Paoton Model, Law of Conservaton of Energy

Planck es quantum hyyothesis that energy ias emited and absorbed in discrete amounts. Albert

Einstein yut yhysical meaning into Planck es quantum hyyothesis by elylaining the yhotelectric eiect

as the evidence for quantsaton E =hf). The Photoelectric eiect is the eedecton of electrons from an

electrode by incident light ak a light that is shone at a syecifc frequency onto a yiece of metal

causes electrons to foi or if a certain metal ylate is irradiated iith light at a certain frequency, an

electron iill be eedected ihich can be detected ihen it interacts iith a yositvely charged iire). The

light must have a minimum/threshold/critcal/cut oi frequency f0) for the electron to be emited l

interceyt of mal k inetc energy vs frequency on grayh). The ability for the electron to be eedected

deyends only on frequency and not on intensity. +f the yhoton energy is greater than the iork

functon this goes into the k inetc energy of the released electron.

Philiy Lenard observed that the frequency of the light caused a yhotocurrent through shining UV

light through a quartz screen onto a zinc ylate iith variable voltage inside a vacuum tube and

observing the current induced.

Elyeriment:

He observed that the yhotoelectric current same as the rate of emission of electrons) is directly

yroyortonal to the intensity of light falling on the electrode but, to obtain zero current, the voltage

has to be reversed to a certain V0 k noin as the stoyying yotental. The voltage must be reversed to

such an eltent that the electrons cannot reach the anode. This is the malimum k inetc energy an

emited electron can achieve. He found that the intensity of the light did not imyact their energy.

The larger the number of electrons, the greater the yhotocurrent. The intensity of light is the

number of incident yhotons no. yhotons hitting metal) not frequency.

Einstein in 1905 used a model iith tio nei ideas to elylain the yhotoelectric eiect: 1921 Nobel

Prize

1. Lai of conservaton of energy

2. Planck es quantsaton E =hf) of light yhotons

Einsteines model has:

1. Energy of light is unevenly syread out over iavefront but concentrated in ‘yack etse or

‘burstse yhoton)

2. Each yhoton has energy given by E =hf, it cannot yossess all amounts of energy, rather it is

limited by certain discrete values hence causing ‘yack etse

. A yhoton could give uy all or none of its energy to one electron. The yhoton could not give a

yart of its energy iave model of light said energy could build uy) i.e. all or nothing

4. One yhoton can liberate one electron as long as it can overcome the iork functon – there is

no tme gay

+t elylained hoi electrons could be eedected iith very loi intensity incident light at the right

frequency, because it only tak es one yhoton at the right energy to k nock out an electron and also

hoi increasing the intensity, increased the current but not the stoyying voltage as greater intensity

means more yhotons, but not more energetc yhotons – therefore more interactons yroduce more

current but the average energy of the electrons is unchanged. +t also elylained ihy increasing the

frequency caused the stoyying voltage to be increased linearly as a greater frequency greater

energy of yhotons E = hf) therefore each yhoton can transfer more energy to an electron.

Elamyle analogy:

Electron sitting on a solar yanel. No electricity foiing as electron doesnet move iithout light but,

once sunlight hits the electron at the right frequency NOT +NTENS+TY then the electron moves and

electricity starts foiing enough energy to move aiay from atom) above threshold the electron iill

have more energy but the electron has malimum KE. +t doesnet build uy, meaning that if you shine

irong frequencies on it, it doesnet mak e small amounts of energy build uy so it moves, rather

nothing hayyens.

Photons have iave-yartcle duality, meaning

that they have both the yroyertes of a iave and

a yartcle.

On a grayh iith KE on the y alis and frequency

on the l alis, the threshold frequency is the l

interceyt value ihereas the iork functon is the

negatve y interceyt value. All three lines have

the same sloye, Planck es constant.

The quantum model resolves the UV catastroyhe as

Lai of Conservaton of Energy:

hf = KEmal + ф total yhoton energy = malimum energy converted into k inetc energy of electron +

energy required to overcome electron binding forces

Work functon: E = hf0 y interceyt of mal k inetc energy vs frequency on grayh) minimum

energy/energy at threshold

+Q 4 Syecial Relatvity

+n 1905, Einstein irote 4 yayers, one ias on syecial relatvity ihich did aiay iith the aether the

medium assumed light travelled through) and there ias no absolute reference frame. Einsteines

syecial relatvity ias based on tio yostulates yroyositons). Syecial relatvity only concerns things

in uniform moton or statonary inertal frames of reference).

1. Princiyle of Relatvity

The lais of yhysics are the same in all inertal at rest or at constant velocity) frames of

reference i.e. no aether ias required as there is no absolute reference frame for ihich to

comyare our moton to, everything is relatve there is no universal directon. You cannot do

an elyeriment to determine ihether you are statonary or in constant moton. both

observers and movers have to insist they are not moving)

2. The syeed of light [c] has the same value in all inertal frames in a vacuum. The syeed of light

does not deyend on the syeed of the source or the observer syeed doesnet mater ihether

+em moving the torch or not). C is constant in a vacuum.

htys://iii.youtube.com/iatchdv=WdfnRWigbd0

Evidence for yostulate 1:

Michelson and Morley Elyeriment

They intended to fnd the aether through shoiing that lightes syeed ias diierent ihen they rotated

the set-uy aether remained in the same directon) as one directon iould be in the directon of the

aether iind faster) and one directon iould be going against it sloier) thus, causing a change in

the interference yatern as ihen the refected rays combined they iould move at diierent syeeds.

Hoiever, there ias none.

Result: null result

Light ias thought to require a medium aether ihich ias considered to be fled), stars and ylanets

iere believed to be moving through the aether. Einsteines 1st yostulate did aiay iith the aether.

The null result did not suyyort the hyyothesis.

(or yostulate 2, c is constant regardless of frame of reference of observer and source of light

0.1 - 0.9c the bigger the diierence betieen tio events same frame = same syeed but once

diierent syeed then things hayyen to tme)

Simultaneity – tio observers may disagree on simultaneous nature of event

Syeed of light in a vacuum is constant

Time Dilaton

The reducton in the rate at ihich tme yasses in a frame moving in relatve moton to the observer

T aliays bigger that T0 botom constant aliays less than 1. Botom c2 iill cancel

(aster through syace, sloier through tme

Syacetme

Syacetme includes dimensions of syace deyth z), length y), iidth l)) and 1 dimension of tme

t), 4 dimensions in total. These 4 dimensions coordinate events in syatal reference at a syecifc

tme. All inertal frames have this.

+t reinforces Postulate 2.

Time and distance are relatve, meaning that tme and distance have diierent values deyending on

measurement by diierent observers in diierent frames of reference. As c = d/t, distance and tme

must adedust so c remains constant. Physicists agree that there are no observatons that contradict

Einsteines tio yostulates. Hoiever, lik e all theories, it iill contnually be tested and used untl nei

evidence modifes them.

Time Dilaton and Length Contracton

Einsteines tio yostulates of syecial relatvity mean that observers in tio inertal frames disagree on

measurements. Moving clock s run sloi since c is a constant, tme ayyears to sloi in a moving frame

ihen comyared iith a statonary frame. Only by measuring diierent lengths and/at tmes, could

observers measure light to be travelling the same velocity in each frame.

When V ayyroaches 0.1c to 0.9c tme dilaton becomes observable. Time iould stoy if you travelled

at c, nothing is found that can travel at this syeed.

Describe: ieorge (itzgerald and Hendrik Lorentz

Before Einstein indeyendently suggested an alternatve elylanaton for the null result of the Aether

elyeriment from Michelson and Morley. Their elylanaton ias that all obedects shrink in the directon

of moton relatve to the statonary Aether by a factor. Lorentz sai it as a yhysical contracton of

obedects, Einstein said there ias no yhysical change in length of high-syeed obedects but rather a

change in tme and yerceyton of syace hoiever, factor is correct. Today the equaton is k noin as

the Lorentz (actor or Lorentz-(itzgerald contracton. γ=

1

√1−v2

c2

Time Contracton

t=t 0

√1-v2

c2

ihere t = tme measured in frame of reference in relatve moton outside observer look ing in.

Aliays larger than t0.

Where t0 = yroyer tme or real tme ihere tme measured and observer travel at the same velocity

in the same reference frame), it is aliays smaller than t.

Where the denominator is the Lorentz factor ihich is aliays less than 1. c is syeed of light, v is

syeed of moving frame of reference.

Lengta Contracton

l=l0 √1−v2

c2

The contracton of length is in the directon of moton c ). Where l0 is the real/yroyer length,

length measured for an observer and obedect in the same reference frame

Where l = contracted length of the obedect measured from a diierent reference frame. shorter than

l0)

Evidence:

Observaton of Cosmic Origin Muons at Earta’s Surface

When Einstein yroyosed the theory of tme dilaton in 1905 there ias no elyerimental evidence,

since that tme, a large amount of elyerimental evidence has been collected. Muons are sub atomic

yartcles created by cosmic ray collisions sunlight beams collide) 15k m above the Earthes surface

uyyer atmosyhere). The muon is unstable, a statonary Muon has an average lifetme measured by

an atomic clock of 2.196 micro seconds. Muons travel at 0.9997c.

Hoi can ie detect muons on Earth if they theoretcally decay before they reach the Earthes surfaced

Time dilaton. Using s = vt, from yersyectve of the muon, s = 0.9997 l l 108 l 2.196 l 104, the muon

should only be able to travel 658 m. But, measured from earth…

Elyand and ylace diagram

Atomic Clocks - Hafele-Keatng Experiment

+n 1971 they yerformed the Hafele-Keatng elyeriment to test Einsteines theory of relatvity and tme

dilaton. There are 4 Caesium atomic clock s, 2 in edet ylanes that fei tiice around the iorld and 2

on the ground. The edet ylanes frst fei east same directon as the Earthes rotaton) and then fei

iest.

Time dilaton theory states a greater tme dilaton occurs ihen the edet ylanes fei iest because

there is a greater relatve moton v) betieen the earth and the edet.

+t ias yredicted that clock s that fei east iould lose 40ns tme on moving clock is less than earth

clock /ran sloi) and clock s that fei iest iould have a tme dilaton of 275ns tme on earth clock is

sloier than tme of moving clock as the earth clock is moving iith the earth earthes velocity +

ylane) but the ylane is moving against the rotaton of the earth ylane-earthes velocity) thus, in

relaton, the earth clock travels faster than ylane clock as higher syeed = higher tme dilaton). When

the ylanes landed, the actual results iere 10% of the calculated yredicton and therefore

elyerimentally confrmed tme dilaton.

Partcle Accelerators

Time dilaton has been tested in high syeed yartcle accelerators such as Large Hadron Collider. As

tae speed of tae caarged partcles suca as protons approaca c, an increase in tae lifespan of

subatomic partcles has been measured and tme dilaton confrmed same as Muon yhenomena).

This yrovides elyerimental evidence for yredictons of the theory of syecial relatvity tme dilaton

formula, length contracton formula).

Elyerimental evidence for yredictons of the theory of syecial relatvity tme dilaton formula,

length contracton formula) can be observed in elyeriments from cosmological studies. The

behaviour of light from distant suyernovas, binary stars, gamma rays all confrm Einsteines theory.

Syeed of gamma rays emited from radioactve decay shoi ihen subatomic yartcles travel near c.

The gamma rays emited also travel at c to an observer.

Elylain

Light from binary stars reach earth at c, their relatve moton changes f of light but not v.

Suyernovae decay yroducts yartcles) from the elylosion travel at % c and light reaches the earth

and yeryendicular to the line of sight from earth at the same tme. +f velocity of the source changed

the syeed of c, the light emited from yartcles moving toiards the earth iould reach the earth

faster but, they do not.

Reinforces yostulate 1.

Consequences and Ayylicatons of Relatvistc Momentum Momentum dilaton)

When an obedect moves at syeeds much less than c, it has a Neitonian momentum y = mv). As the

obedect moves at relatvistc syeeds 0.1c+) it iill have a greater momentum. As ie ayyroach c, ie

must modify Neitonian mechanics to account for the relatve nature of syace, tme and

momentum.

Relatvistc momentum can be derived from Newton’s 2nd law.

Defning acceleraton as, a=ΔvΔt , it can be elyressed in terms of momentum:

F=ma = m(∆vΔt ) =

ΔpΔt

The defniton of force must be the same in all inertal frames as yer Einsteines 1st yostulate

thus, ΔpΔt

must be constant for all observers

The defniton of ( relies on tme as F=ΔpΔt

thus, tme dilaton must be accounted for:

F {proper time }=pt0

=m0v

t0

F {relativistic }=pvt v

=

pv √1−v2

c2

t 0

(yroyer tme needs to equal (relatvistc for Einsteines 1st yostulate to be satsfed.

F=m0v

t0=

pv √1−v2

c2

t0

∴Pv=m0v

√1−v2

c2

Where:

Pv is the relatvistc momentum of an obedect moving at v measured by an observer in Ns -1 or Kg-1m-1s-1

Pv aliays > P0

m0V is the Neitonian momentum, a loi syeed ayyrolimaton of a body in momentum.

m0 is the rest mass of the obedect unaiected by mass dilaton. +t is measured in the frame of

the obedect.

Mass dilaton: mass is a relatve quantty. Obedects iill have a greater mass ihen in moton at

relatvistc syeeds 0.1-0.9c) in comyarison to ihen it is statonary due to relatvistc momentum.

As an obedect ayyroaches c the relatvistc momentum Pv ayyroaches infnity. mass ayyroaches

infnity due to mass dilaton. i.e. Pv ayyroaches 0 ihen obedect ayyroaches c, so mv ayyroaches

infnity. Thus, ie can never reach the syeed of light as the momentum of the yroton ayyroaches

infnity causing a loss in syeed.

Pv has been confrmed in the LHC in collisions betieen sub-atomic yartcles. The relatvistc

momentum of yrotons travelling at 99.999999%c is 8000l greater than the P = mv yredicted by

Neiton. These yrotons have a mass 8000l greater than a yroton at rest.

Limitaton on Malimum Velocity of a yartcle imyosed by SR

An infnite amount of force iill be required to accelerate an obedect to c therefore, it is imyossible for

a material obedect to travel at c iith resyect to an observer thus, c is the syeed limit of the universe.

Time dilaton and length contracton also indicate c as the natural velocity limit.

An obedect ayyroaching c has its tme sloied to 0 and length in directon of moton contract to one

ylane height and deyth remain the same but, length contracts). (rom the obedectes frame of

reference, the universe rushes toiards the obedect, tme ayyroaches 0 and universe iould shrink to a

ylane in the directon of moton.

(or a light yhoton, tme has no meaning and the universe has shrunk to a ylane in directon of

yhotones moton, the yhoton is at the start and end of its edourney simultaneously, there is noihere

to go and no tme yasses. The yhoton is annihilated created and destroyed simultaneously at one

yoint in syacetme)

(rom the Earthes frame of reference, ie see the yhoton travels ayyrol. 8 minutes our yersyectve),

travelling at c yhoton yersyectve, real syeed) untl it reaches its destnaton and disayyearing ihen

it gives its energy to an atom.

As an obedect ayyroaches c, its relatvistc mass increases, the energy suyylied to mak e the obedect

travel faster is converted to mass thus, stoyying the yhoton from reaching c.

Mass Energy Equivalence Relatonshiy

E = mc2 tells us that mass and energy are interrelated i.e. mass has energy and energy has mass.

E = mc2

Where E = energy in J

m = mass in k g or eV

c = syeed of light is ms-1

+n the Large Hadron Collider LHC) it is the energy of the yartcles that mater, not their mass. +n the

LHC, the more energy yotental/k inetc), the more massive the nei yartcle that can be made.

Producton of Energy by tae Sun (fusion)

All stars convert mass to energy in their core by fusion reactons. main fusion reactons are:

1.

The above reactons have been in the sun for 5 billion years and have another 5 billion to go.

Hydrogen nuclei are fused together and afer several steys, helium nucleus is formed iith the

release of ayyrol. 25 MeV.

SEE MOD 8

Our star is a 2nd or rd generaton star, formed from remains of other stars that elyloded earlier in

our galaly. As the nebulae contracted due to gravity, the yressure and temyerature at the core

sustained the above fusion reactons.

Partcle and Ant-Partcle Interacton (Anniailaton)

Paul Dirac in the 1920s iork ing on quantum mechanics suggested every yartcle had an ant-yartcle

iith the same mass but, oyyosite charge - elceyt yhotons massless). Eg: electron and yositron

Positrons are yroduced ihen a yroton decays to a neutron. +f the yositron collides iith an e -

annihilaton occurs and tio gamma rays γ) are yroduced. Annihilaton occurs in the Large Hadron

Collider LHC)

e− + e+ → γ + γ

Charge is conserved i.e. e-+e+ = 0), gamma rays have no charge

Momentum is also conserved momentum of e- + momentum of e+ = momentum of γ rays.

Waat about mass?

The electron and yositron both have mass, because γ rays do not – it may ayyear that mass is not

conserved hoiever, E = mc2 shois the mass of the electron and yositron are converted into

energy ak a γ rays.

How is it used?

PET scans: yositron emission tomograyhy

Radioisotoyes are inedected into the body tssues iith glucose such as brain

+sotoyes atach to glucose ihich can be detected as it causes γ rays to be emited through

annihilaton

Patent is ylaced in a ring-shayed detector

Tissues iith high actvity have more γ rays emited ihereas ylaces iith loi actvity gloi

less under detecton

Used in Alzheimeres detecton

Combuston of Conventonal Fuel (Caemical Combuston)

E = mc2 ayylies to nuclear reactons fusion), chemical combuston, mass-energy reactons.

Hoiever, the mass diierence is miniscule thus, not noted.

Combuston: chemical reacton ihere electrons are elchanged betieen atoms but nuclei are not

involved.

Heat of combuston for coal is 4 MJk g-1 = .4 l 107 J of heat energy is yroduced ihen 1 k g of coal is

burnt.

E = mc2 = ∆ E = ∆ mc2 = .4 l 107

∆m = E/c2 = .4 l 107/ c2 = .8 l 10-10 k g = .8 l 10-8 % of original mass

Rank ings of energy:

1. Annihilaton of mater-antmater all mass converted to energy)

2. (usion some mass converted to energy)

. Combuston insignifcant amount of mass converted of energy)

Syectroscoyy Practcal 2/6/20

Aim: (ind out ihat the syectral lines of Hydrogen look lik e

Risk assessment:

Risk +dentfed Hazard Risk controlled

+nducton coil Produces X-rays thus, medium-high risk High voltage

Stand over a metre aiay so X-Ray contact is minimisedAdedust iires only ihen yoier source is turned oi to yrevent electrical accidents or burns

Discharge tube ilass tube can break loi-medium)

Tak e care ihen handling tube and iear goggles and leather closed shoes

Syectroscoye Retna damage loi-medium) Donet look directly at sunlight, only at fltered sunlight or fuorescent light

Metaod:

1. Connect negatve DC terminal of transformer to negatve terminal of inducton coil

2. Connect the yositve terminal of transformer to yositve terminal of inducton coil using

alligator cliy ended iires

. Connect negatve outyut terminal of coil to toy of discharge tube and yositve to the botom

of the discharge tube

4. Adedust the ylates at the toy of the coil so the gay betieen them is about 5cm iide so no

syark ing iill occur

5. Turn on the yoier suyyly to 6 volts

6. Using a syectroscoye, viei the Hydrogen discharge tube do not yoint syectroscoye at the

sun)

7. Adedust the clarity of the syectral lines through eltending, retractng or changing the angle of

the syectroscoye

8. Note colours of syectral lines

Diagram:

Results:

Hydrogen Syectrad 4 lines, Red, yelloi, cyan, violet

Sunlight syectrad A contnuous syectrum rainboi)

(luorescent syectrad Mercury gas, 5 or 6 lines, Red orange green teal blue indigo

Syectroscoyy:

(or emission syectroscoyy, you must have an elcited gas through yassing electricity in it thus,

emitting light

1. Hoi can the syectra of stars yrovide informaton ond

2. Surface Temyerature

. Rotatonal and translatonal velocity

4. Density

5. Chemical comyositon

Conclusion:

1. Emission syectra are the distnctve iavelengths a certain element emits ihen in an elcite

gaseous state. They are yroduced through yassing electricity through an elemental gas in a

discharge tube, causing the gas to emit light. This light is then vieied through a

syectroscoye ihere a yrism sylits the light into its distnctve iavelengths, giving us

informaton on the comyositon of certain comyounds.

2. The Hydrogen syectrum consists of 4 coloured bands. (rom lef to right there is: red

656nm), yelloi-green 486nm), cyan 4 4nm) and violet 410nm).

Hoi does the syectroscoye iork d Hoi does it yroduce a syectrumd

Module 8 From the Universe to the AtomThe Big Bang Theory BBT) is used to elylain formaton of elements on the yeriodic table during 1 .8

billion years and is an atemyt to understand origin and develoyment of the universe. According to

the BBT, energy syread out from a singularity a small yoint of high temyerature and density) before

the singularityd conedecture. Brian Smith disyroved the collaysing universe theory through shoiing

that the universe ias elyanding at an increasing rate. As energy syreads over increasing distances,

the temyerature greatly reduces from that of the singularity. Partcles Quark s, electrons, neutrons,

yrotons) and forces mediated by yartcles gravity all yartcles, electrostatc charged yartcles,

ieak nuclear forces quark s, yhotons and leytons electrons), strong nuclear forces gluon

bonds that hold quark s), quark s) all form out of energy. At loier temyeratures d/t universe

elyansion, yartcles formed become stable and combine to form atoms/molecules – mater. Energy

from singularity is all the energy in the universe and for 1 .8 B years this energy has been

transformed into radiaton and mater observable today. Total amount of energy is the same as the

beginning.

Atoms iere thought to be the smallest, indivisible yartcles untl electrons and radioactvity iere

discovered. Later elyeriments shoied that yrotons and atoms iere divisible and made from quark s

but, electrons are not elementary). There is an antyartcle for every yartcle, slightly more mater

than antmater ias formed ihyd No idea. Most of ihat ie detect today is mater not antmater.

Mater and ant-mater annihilate ihen they collide, ihen electron + yositron = annihilated and 2

gamma rays released.

Energy lef over from the BBT that did not form into mater can be detected as cosmic microiave

back ground radiaton CMBR). BBT yredicts gamma rays due to elyansion of the universe are seen

as microiaves. Robert Wilson and Arno Penzias measured and confrmed this using COBE satellites.

Evidence is required to determine ihether the universe is elyanding, contracton or statc. There

are models of the universe:

(lat universe – elyansion slois and stoyyed

Oyen universe – elyansion accelerates

Closed universe – elyansion eventually reverses and contracts

Evidence:

Einsteines general theory of relatvity eltended the syecial theory to acceleratng reference frames

and gravity the iarying of the fabric of syacetme). Russian mathematcian Alelander (riedmann in

1922 and ieorges Lemaitre yredicted elyansion of the universe. The syace betieen galalies is

elyanding i.e. lik e dots on a balloon therefore, BBT is not an elylosion but an elyansion of syace as

galalies are not moving through syace rather, syace betieen them is elyanding.

Evidence:

Hubble using Ceyheid variable stars intensity variable suyergiants iith a yeriod related to

luminosity) in the Andromeda ialaly, elyanded on Henrietaes iork ihich shoied that the

absolute velocity of the star and intensity of light reaching observer are k noin, the inverse square

lai can be used to fnd distance to the star. (inding distance to individual stars, Hubble calculated

syeeds of nebulae and galalies from Earth by comyaring iavelengths of syectral lines of atoms

Hydrogen) he notced the elongaton of iavelengths red shif, nebulae moving aiay) due to the

Doyyler Eiect.

Hubble Relatonshiy:

The further aiay the galaly, the faster it is moving aiay from Earth. iRAPH Recessional Velocity vs

Distance

iradient = Ho Hubblees constant k m/s/MPC)

∴ v =d/t, t = d/v = 1/H0 = age of the universe

V = H0d

Where:

v = recessional velocity k m/s)

H0 = Hubblees constant 70 k m/s/MPC) estmate of universees syeed of elyansion, galaly at a

distance of 100 MPC is travelling from Earth at 7000k m/s

D = distance to the galaly MPC)

Other evidence:

Red shif of nebulae

AU is distance from sun to the earth = 1.5 l 10 11m

……..

E = mc2 and Nuclear Reactons in Stars

Energy converted into yartcles

Mater, ant-mater reactons in frst minutes of BB

More mater than antmater 1:1 B one eltra yartcle yer billion

That is all mater in yresent universe

Nuclear Synthesis yroduced Hydrogen, Helium, Lithium

00 000 yrs afer BB, electrons combined iith H, Li, He to form atoms

The nelt 1 .8 B yrs, elements from He to (e iere yroduced by fusion reactons in core of

stars

Elements heavier than (e iere yroduced in fusion reactons in suyernova elylosions

Our sun formed from the gravitatonal collayse of gas and dust from earlier suyernova

elylosions and dead stars

Heavier earth elements eg: Pb iere concentrated in terrestrial rock y) ylanets

Stars frst form 400 million years afer BB from mater accreton d/t gravity

(usion of H to He early stars being very large and hot burnt out quick ly and suyernova

elylosion

Calculatons on the mass and energy outyut of our sun found amount of energy yroduced

yer atom ias > 1 l 108 tmes energy yroduced by chemical reacton combuston) rather it

must come from E = mc2 through fusion of H to He mass-energy equivalence)

Emission:

Each transiton has a syecifc colour shell 6 to 2 is violet etc…) ie can see everything untl

2nd orbital hoidd iith nei model of the atom

Evidence for elyansion, fusion hoi does that yrove BBTd

Absoryton: syecifc iavelengths of light are missing from contnuous syectrum e = hf)

Black body radiaton yroduces a contnuous syectrum containing all iavelengths. As black body is

heated, the iavelength of ihich most radiaton is emited decreases and yoier radiated increases

intensity) i.e. a syread of energies emited. Therefore, as temyerature increases, yeak iavelength

decreases colour changes from iarm to cool

Quanttated by Wienes lai:

Mal iavelength = b/t

When yeak iavelength of a syectrum is green, blue light is also emited therefore, green is seen as

ihite.

Absoryton syectra from all stars is similar to our sun indicatng similarity in chemical comyositon

and reactons occurring iithin them basic chemistry and yhysics ayylies throughout the universe).

There are diierences but no nei lines have been discovered in other stars.

b = 2.898 l 10- mk

Which elements are elyected to occurd

OBA(iKM – oh be a fne guy k iss me

Stars are classifed by yresence of absence of syectral lines.

Diierences betieen star grouys iere due to atoms becoming ionised losing electrons) at certain

temyeratures. At cooler temys red stars) does not have enough energy to elcite atoms enough for

them to fuse and mak e nei elements thus less syectral lines emited.

Astroyhysicists originally used an alyhabetcal system based on absoryton syectra, the main

diierence for diierent absoryton lines is due to stares temyerature. The uydated classifcaton

system used is the Morgan Kennan System ihere same leters OBA(iKM) are used but based on

syectra lines yroduced and temyerature hot 0,1, 2, , 4, 5, 6, 7, 8, 9 cool) and subdivided further,

temyerature given numbers and luminosity is given roman numerals +a, +b, ++, +++, +V, V). Our sun is

i2V. +t allois us to classify more stars in greater detail. Absoryton is used as it does not require full

atom, easier and more accurate. Use absoryton to classify stars

Hertzsyrung Russell Diagram

Eednar Hertzsyrung in 1911 grayhed absolute magnitude v colour. Henry Russell in 191 grayhed

absolute magnitude of stars v syectral class. Both found that stars iere grouyed on the H-R

diagram.

Using the nak ed eye, brightest stars iere given absolute magnitude of 1. Less bright stars iere

yositve values 1, 2, least-brightest etc). Brighter stars iere then discovered later and assigned

negatve values. Absolute magnitude is a measure of luminosity all stars at the same distance).

Relatve magnitude measure hoi bright the star ayyears from earth stars at diierent distances).

Luminosity measures total energy radiated by a star yer second log scale). Reyresented by a

number on the absolute magnitude scale corresyonds).

On the main sequence, stars fuse hydrogen helium in their core and have a luminosity class of V,

red giants fuse heavier elements and have luminosity of +, ihite diarfs are hot, condensed remains

of stars that have deyleted nuclear fuel

Life cycle of a star:

Stellar nebula average star red giant ylanetary nebula ihite diarf

OR

Stellar nebula massive star red suyergiant suyernova black hole OR neutron star > 8SM)

Tyyes of Nucleosynthesis Reactons mak ing of atoms) in Main Sequence and Post-

main Sequence Stars

Defne:

Nucleosynthesis: nuclear fusion of light nuclei H) to form heavier nuclei He) iith this yrocess

contnuing. On earth ie cannot do fusion commercially, only fssion due to high yressure and energy

require. This is yossible because very high temyerature and yressure in stars. Every element has

been synthesised in the core of stars.

Describe:

Self-sustaining fusion reactons release more energy than required to start them/ignite elothermic)

eg: fusion reactons uy to (e 26), non-self-sustaining fusion reactons require larger amounts of

energy and yroduce elements heavier than (e 26). These occur in the core of suyernovas 8l

heavier than our sun) that collayse then elylode or neutron star collisions.

Elylain:

A star is comyosed of mainly H nuclei 11 H) and He 4

2He) nuclei 2 yrotons, 2 neutrons).

2 fusion reactons occur.

Main Sequence:

P-P Chain

+n main sequence stars i/ mass < 1.5 solar masses and core temyerature of < 18 000 000K. (usion

reactons occur to yroduce energy from fusing H and He yroton-yroton chain) ihich is the main

fusion reacton 85% of our sunes energy). There are other P-P chain reactons, the sun yroduces 98%

of its fusion reacton created energy using P-P chain reactons.

KNOW TH+S:

11H +

11H→

21H deuterium) + e+ yositron) + v neutrino)

21H deuterium) +

11H→3

2He helium ) + γ gamma ray)

32He helium ) +

32He→

42He stable Helium) +

11H +

11He

∴ Net reacton aggregate reactants and yroducts) is:

4 11H 4 yrotons) →

42He + 2e+ 2 yositrons) + 2v 2 neutrinos) + 2γ 2 gamma rays)

Mass number is on the toy and atomic number constant) is at the botom. Those change deyending

on tyye of radioactve decay undergone.

CNO

+s a cyclic reacton ihere C is fused to N to O and then back to C occurring in the core of stars i/

mass > 1.5 solar masses and core temyerature of stars > 18 000 000K. This same net reacton occurs

for the CNO cycle elceyt iith gamma rays released, mak ing it higher energy.

4 11H 4 yrotons) →

42He + 2e+ 2 yositrons) + 2v 2 neutrinos) + γ 2 gamma rays)

Our sun only yroduces 2% of its energy using CNO but stars > 1.5 solar masses yroduce most of their

energy by this cycle. The C, N, O act as catalysts assist reacton) convertng 4 yrotons to He.

*start 1216C carbon) +

11H yroton) →

137N nitrogen) + γ gamma ray)

137N nitrogen) →

136C carbon 1 ) + e+ yositron) + v neutrino)

136C +

11H→

147N nitrogen 14) + γ gamma ray)

147N+

11H→

158O olygen 15) + γ gamma ray)

158O →

157N nitrogen 15) + e+ yositron) + v neutrino)

157N+

11N→

126C+

42He* back to start

Rays, elements emited are dictated by tyye of radioactve decay alyha, beta, gamma)

Other:

When stars leave the main sequence, the heavier elements gather at the centre of the star layers

of an onion.

Our sun is not large enough to fuse elements heavier than Helium. +t iill end energy yroducton i/ a

core of Carbon and Olygen.

P-P chain and CNO yroceeds to… ihen He becomes maedority fuel iithin the core

42He+

42He→

84Be beryllium)

84Be +

42He→

126C carbon 12) + 2γ gamma rays)

126C +

42He →

168O olygen) + γ gamma ray)

These reactons yroduce C and O atoms essental for life. Larger stars fuse heavier elements ihich

require higher temyerature and yressures to overcome the electrostatc forces. (or the largest stars,

fusion stoys iith core of (e and gravity collayses the star, causing the star to suyernova ihich

yrovide the energy to fuse all other elements uy to U 2 8). All elements yroduced are syread

throughout the universe thus, alloiing the creaton of nei stars. Very large stars > 8SM) can

collayse to form:

Neutron star – diameter of ayyrol. 0k m iith same mass as our sun very dense), all

electrons and yrotons have collaysed to form neutrons elements emited)

o Pulsars – regular yulses of radio iaves and visible light from a rotatng neutron star

Black holes – >20SM) even neutrons in a neutron star collayse due to the force of i being

so strong, forming a singularity meaning a yoint of infnitely small volume and infnite

density more massive, the greater the gravity), even light canet escaye from it black hole)

Every galaly has a black hole at the centre.

Event horizon: radius around singularity ihere the escaye velocity elceeds C

8.2 Elyerimental Evidence Suyyortng the Electron

The discovery of the electron ias made afer decades of elyerimental observaton and inferring

models of the atom. +n 1857 Heinrich ieissler invented the glass vacuum tube.

Early Elyerimental Evidence Suyyortng the Electron

Cathode Rays

Discharge tube: A discharge tube has a vacuum inside and tio metal electrodes, a cathode fve cent

yiece) -) and anode +). At standard temyerature and yressure STP) air is an insulator, at reduced

yressure, air/all gases conduct electricity. iases can also be made to conduct by yassing electricity

through it 100 000+ V).

Aim: ihat are the diierent yroyertes of cathode rays that can be observed using discharge tubesd

Describe:

+nducton

coil

Risk Identfed Hazard Risk controlled

+nducton coil +f a syark edumys there iill be elyosure to harmful EMR X rays and iamma rays)Burning and electrocuton

Stand back 2 m to yrevent elyosureDo not ylace hands near yointers ihen electricity is onOyen yointers so no syark occursOyen inducton coil 5cm to reduce voltage induced

Discharge tube Break ing glass can yose risk of cuts

Closed shoes, handle tube iith care, ylace tube in the centre

1. Connect DC negatve terminal of the transformer to the negatve terminal of the inducton

coil

2. Connect DC yositve terminal of the transformer to the yositve terminal of the inducton coil

. Seyarate yointers by a 5cm gay to yrevent a syark on the inducton coil

4. Using an alligator cliy ended iire, connect the yositve terminal of the coil to the anode of

the defecton tube.

5. Using an alligator cliy ended iire, connect the negatve terminal of the coil to the cathode of

the defecton tube.

6. Siitch on the yoier suyyly and adedust voltage to 4-6 V

7. Hold a bar magnet yeryendicular to the cathode ray iith the north yole facing the beam

8. Move it closer and further from the ray and observe changes in the ray

9. Hold a bar magnet yeryendicular to the cathode ray iith the south yole facing the beam

10. Reyeat steys 1-5 iith connecton to the Maltese Cross tube

11. (liy the Maltese Cross uy by tltng the tube

12. Turn on the yoier suyyly

1 . Observe yatern formed on glass surface behind the Maltese Cross

14. (liy the Maltese Cross doin by tltng the tube

15. Turn on the yoier suyyly

16. Observe yatern formed on glass surface behind the Maltese Cross

17. Reyeat steys 1-5 iith connecton to the Paddle Wheel tube

18. Turn on yoier suyyly

19. Observe moton of the yaddle iheel

Deflecton tube observatons: As yer the RHR the cathode ray defects ihen interactng iith a

magnet thus, the beam is diierent to light as light does not interact iith a magnetc feld. To react

to a magnetc feld as yer the RHR, the ray must be charged.

Maltese Cross tube observatons: When the cross is uy a black shadoi of the cross is yroedected on

the anode side of the tube indicatng the beam originates from the cathode -) and that the cathode

ray cannot yass by solid. +ndicates that the cathode ray cannot bend 90o travels in a straight line).

Similar to light as it forms shadois, travels in straight lines and rays. When cross doin, bright

shadoi due to diierent elyosure of the anode glass to the ray.

Paddle Waeel tube observatons: +ndicates the cathode rayes yartcles have mass, velocity and thus,

momentum they are yhysical) as the ray is yhysically hitting the iheel - ayylying an elternal force

ihich mak es the iheel turn. The yartclees energy is indicated through the gloi of the yhosyhor

fuorescent yaint ihich indicates a transfer of energy and momentum from yartcle to yaint.

Explain waat tae saadow of tae Maltese Cross suggests about tae way Cataode rays travel.

The shadoi of the Maltese Cross occurs on the anode side of the cathode ray tube ihich indicates

that the cathode ray is travelling from the cathode to the anode as if the ray from travelling in the

directon from the anode to the cathode, the shadoi iould be yroedected on the cathode side of the

discharge tube. The shadoi also indicates that, lik e light – cathode rays cannot bend 90o because if

they iere able to bend 90o, the ray iould reach the anode iithout being block ed by the Maltese

Cross, hence no shadoi iould occur. The shadoi also suggests that Cathode Rays cannot travel

through solid obedects, as they are block ed by the Maltese Cross hence, causing a shadoi.

Will Cataode rays be deflected if taey are parallel to magnetc felds? Discuss.

Defecton

Shadoi Maltese Cross

Cathode rays iill not be defected if they are yarallel to a magnetc feld as the charged yartcles

must have a yeryendicular comyonent of their moton/velocity relatve to the B feld to elyerience a

force, as yer the RHR.

Waat aappens to tae cataode ray waen a magnetc feld is brougat close to tae ray? Describe bota

Norta and Souta poles.

When a magnetc feld is brought close, yeryendicular to the velocity of charged yartcle iith the

north yole closest to the cathode ray, the ray iill elyerience an uyiards force as yer the RHR. With

the south yole closest to the cathode ray, the ray iill be defected doiniards as yer the RHR.

Way did we aave to use tae inducton coil in tais experiment?

Our elyeriment requires a high voltage thus, an inducton coil is required to increase the voltage of

our yoier suyyly.

Evaluate Millik anes oil droy elyeriment

Cathode Rays

Cathode rays come out from the cathode -) and connected to negatve terminal of the

inducton coil.

Travel in straight lines Maltese cross), yartcle and iave yroyerty

Cause glass to fuoresce a light green colour vacuum)

Defected by electric and magnetc felds defecton tube) a charged yartcle yroyerty

Carry energy and momentum yaddle iheel) yartcle yroyerty

Yelloi cathode ray is due to the ‘coloure of the vacuum

Therefore, Cathode Rays electrons) are yartcles iith a iave-yartcle duality

Evaluate Thomsones charge to mass elyeriment ½ yage

Thomsones Charge to mass elyeriment

+n 1897, JJ Thomson yroved cathode rays iere electrons and measured their charge and mass q:m

rato). The rato is integral and = q:m = 1.76 l 1011 C. Thus, the q:m rato ias used to yrove the

elistence of electrons. The very high rato shoied that electrons had a large charge but miniscule

mass.

Elylain: Thomson used a cathode ray tube iith tio felds yarallel electric ylates), magnetc feld

electromagnet). The felds are 90o to each other.

Electric feld defects the cathodes ray uy, magnetc feld defects cathode rays doin. Electric feld (

= qE) and magnetc feld ( = qvbsinθ) are adedusted so that forces cancel out and the beam is

undefected. Undefected beam is used to fnd velocity of cathode ray qvB=qE) v = E/B

1. ( = qE = qvB

2. (B = qvB = (centriyetal = mv2/r

. qvB = mv2/r q/m = V/Br

Millik anes Milk Droy Elyeriment

His elyeriment yroved that an electrones energy ias quantsed discrete yack ets, set amount),

rather than contnuous. Crucial yart of our understanding of the electron

Describe: Elyeriment consisted of tio chambers iith a yinhole link ing them. An atomiser yroduces

a fne mist of oil droylets) ias syrayed into the toy chamber and oil droys drif doin, leaving the

atomiser, oil droys iere charged by fricton or by X Rays to further ionise oil droys and increase oil

droy charge. Oil ias used because it had a higher vayour yressure iould not evayorate as fast in

the chamber). Microscoye alloied observaton of oil droylets drifing doin into the second

chamber ihich ias connected to a yoier source and had an E feld.

Elylain: When a voltage ias ayylied, the oil droylets could be made to stoy falling

(mg= (qE

mg = qE

mg = q l V/d as E = V/d

q = mgd/V ihere q = charge on oil droy, m = mass of oil droy, V= yotental diierence used to stoy

oil falling, d = distance seyaratng charged ylates, g = gravity

m ias k noin, Millik an used above to calculate the oil droyes charge.

Analyse: Millik an found the smallest unit of charge to be -1.592 l 10-19C one electron rubbed on the

oil droy), iithin 1% of todayes value of -1.602 l 10-19C. Oil droys could have larger electric charge but

only elisted as multyles of this base unit of charge. Crucial to our understanding of electrons.

JJ Thomsones q:m rato of the electron ias elylained by Millik anes elyeriment. That Cathode Rays

iere negatvely charged yartcles electrons. Millik anes oil droy elyeriment quantfed electron

charge as -1.602 l 1019C. This led to the calculaton of the charge on the yroton size of yositve

charge), yositron and mass of electron.

m = 0.0 5 l 10-9

d = 0.0 m

v = 5500 V

1.87l 10-15 C, bigger than value of electron as more electrons removed

Elyerimental Evidence Suyyortng the Nuclear Model of the Atom

JJ Thomsones ylum yudding atomic model atom of yositve charge i/ electrons scatered inside)

had:

1. mass of atom syread out over its area

2. the sea of yositve charge yudding)

. electrons embedded in the yudding

Elyerimental observaton altered this model

8.2.2 ieiger-Marsden Elyeriment

+n 1905, ieiger and Marsden iork ing under Rutherford yerformed an elyeriment ihere alyha

yartcles alyha radiaton, the He atom i/o electrons) ias fred at thing gold leaf. iold ias used

because a very thin layer of atoms ias required and gold can be yressed into a several atoms thick

foil.

Results:

Most alyha yartcles yassed through iith only small defecton but 1/8000 iere defected by

angles greater than 90o due to hitting ‘somethinge ak a the nucleus

+n Thomsones model there should have been no defecton ihatsoever hence, this

elyeriment yrovided evidence for the nucleus

‘it ias as incredible as if you fred a 15-inch shell at a yiece of tssue yayer and it came back

and hit youe

Rutherford concluded that alyha yartcles iere defected through large yartcles because all

the atomes yositve charge and nearly all of its mass ias concentrated in a small dense

nucleus iith electrons orbitng around the nucleus lik e ylanets around the sun. (rom the

results of alyha yartcles, scatering elyeriments, Rutherford estmated the atom size as

having a diameter of

1 l 10-10m and nucleus of diameter 1 l 10-14m

Signifcant/crucial. He ias the frst to yroyose the elistence of the nucleus, seyarate from

electron moton. Limitatons include organisaton of electrons and inability to elylain ihy

desyite electrons acceleratng, they did not radiate energy and fall into the nucleus could

not elylain electron stability)

Chadiick es Discovery of the Neutron

Afer Rutherford 1908-1911) it seemed logical to assume the nucleus contained yrotons and

electrons orbited outside the nucleus. There iere maedor yroblems iith this idea i.e. mass of the

nucleus ias 2l the atomic number Z) and the de Broglie iavelength ias large comyared to small

radius of the atom. Rutherford yroyosed the neutron.

+n 19 0s Walter Bohei and Becca found yassing yartcles through Beryllium gave a tyye of unk noin

radiaton. +n 19 2 James Chadiick identfed this radiaton as Rutherfordes neutral yartcles

neutrons

Neutrons get trayyed in the Parafn ial but, dislodge Protons. (or Protons to be dislodged, they

must have been hit by something of same mass.

Uncharged neutrons iere difcult to detect, a gas chamber detected Protons since Protons can

ionise remove electrons) gas electricity fois, current detected as electrons are moving. Parafn

ial consttutes of Hydrogen atoms and ias used because the unk noin radiaton could k nock

Protons out of it. By ayylying conservaton lais of momentum/energy to the interacton of a

Neutron iith a yroton neutron mass similar to yroton) Chadiick ias able to yrove elistence of the

neutron. Chadiick correctly assumed the alyha radiaton yroduced neutrons by transmutng ) the

Beryllium nucleus to a carbon nucleus.

momentum before = momentum afer

m1u1 + m2u2 = m1v1 + m2v2

neutron + yroton = neutron + yroton

m1u1 + 0 = 0 + m2v2

Why can classical yhysics no elylain the yroyertes of the atomd

Bohr based on Rutherfordes model, Bohr observed syectral lines of Hydrogen in visible region and

yroyosed yostulates

Rutherford Bohr 191 )

Elylained rebounding of yartcles in the gold Electrons move in circular orbit due to

foil elyeriment electrostatc atracton of the yositve nucleus

Could not elylain ihat ias in the nucleus, yartcles of yrotons and neutrons iere not defned at the tme

Electrons only elist in certain stable energy levels orbitals/energy shells) n =1, n=2, n= integer). +n these stable energy shells, electrons do not emit EMR or lose energy i.e. electron could not occuyy betieen energies i.e. n=1/2, n=1 1/2 no ihyd

Proyosed electrons iere ylaced around the nucleus lik e ylanets around the sun, could not elylain their arrangement

Electrons can move from one energy level to another by being elcited or releasing energy. An electron falls doin to a loier shell, releasing energy as EMR e=hf)

Could not elylain ihy electrons did not atract and fall into the nucleus+f electrons iere orbitng the nucleus, they iould have centriyetal acceleraton hence, release EMR resultng in a loss of KE electrons sloi doin and unable to maintain orbit around nucleus collayse into nucleus every atom iould be unstable

Angular momentum L = mvr mass l velocity l radius), L is quantsed

Only yossible to calculate iavelengths 1/λ = R 1/n2

f – 1/n2f) of syectral lines of Hydrogen not

for mult-electron elements eg: helium)

Some syectral lines of Hydrogen iere more intense red, light blue) than others yelloi, green). The Bohr model does not elylain relatve intensites of electron transitons.

Syectral lines iere found to have a number of hyyerfne lines d/t sylitting of energy levels ihich the Bohr model does not elylain.

Zeeman found that sylitting of syectral lines ias caused by a magnetc feld not only hyyerfne

lines) due to electrones magnetc feld syin) and orbital moton Malielles (ormulas) ihich interacts

iith ayylied B feld. +nteracton of tio magnetc felds creates a force that gives transiton more

energy, seyaratng the syectral lines.

Bohres model introduced the idea of quantsed energy shell levels, n = 1, n = 2, n = ihole

numbers) but did not elylain ihy they iere quantsed. Successful models have both yredictve and

elylanatory yoier. Bohres model lack ed elylanatory yoier and limited yredictve yoier Hydrogen)

leading to Schrodinger and Heisenberges quantum models using de Brogliees iork as a frameiork .

Line Emission Series and Balmer Series in H

The emission syectra EMR emited ihen electrons elcited) emit light in full UV and visible range.

Hydrogen atoms have series of 4 syectral lines reyresentng syecifc iavelengths through colour.

+n 1885 Balmer fnd the iavelengths of syectra of Hydrogen using:

Rydberg/Balmer Equaton

1/λ = R 1/n2f – 1/n2

i) ihere λ is iavelength determined by transiton), R is Rydberges constant on

formula sheet, nf is fnal orbital electron ends uy in smaller value), n i is inital shell the electron is

located in ihole numbers)

(ind reciyrocal at the end.

We only see the Balmer series because EMR is released in visible syectrum. Paschen series, Lyman

series, Brack et series, P(und series release EMR in non-visible syectrums.

Series Discovered Spectral region nf ni

Lyman 1906-1914 UV 1 2, 2nd transiton),4 rd transiton) ,5…

Balmer 1865 UV – visible 2 ,4,5,6…

Paschen 1908 +nfrared 4,5,6,7…

Brack et 1922 +nfrared 4 5,6,7,8…

Pfund 1924 +nfrared 5 6,7,8,9…

iround state is aliays loiest energy shell. LBPaBrP, LbePabePa

Line Emission Syectrum of Hydrogen, Quantsed Energy and the Lai of Conservaton of Energy

The Balmer Series for H is caused by electrons moving from higher n i) to loier energy shells nf) of

2.

E = hf allois energy diierence betieen shells to be calculated.

When and electron changes energy shells from higher to loier), it emits energy in form of EMR or

absorbs energy loier to higher):

E = Ei – Ef = hf = hc/λ

+onisaton is the removal of an electron from an atom so that electrostatc atracton is negligible.

iround energy level of the atom electron in the orbit iith the smallest radius 1st shell). The

energy of the yhoton released and its frequency E = hf) ihen the electron changes energy shells is

given by:

E = E1 – E2 = hf, v = fλ, E = hf f = v/λ E = hv/λ = hc/λ

The most energy is required to elevate electron from ground state to frst elcited shell.

The yrocess of yhoton emission is governed by the lai of conservaton of energy LCE), that is

energy cannot be created nor destroyed- only transformed from one form to another. When an

electron moves from a higher to a loier orbital, LCE states that lost energy is transformed to EMR

iith a frequency. Energy of the yhoton is E = hf. +f the yroton ias absorbed by another electron, the

electron iould move to a higher orbital.

Elyerimental Evidence of de Brogliees Mater Waves

De Broglie iins the 1929 Nobel Prize for his discovery of the iave nature of electrons that elylained

their stability. De Broglie yroyosed that yartcles electrons, yrotons, neutrons that form mater)

have iave-yartcle duality. To describe iave-yartcle duality quanttatvely, the formula can be

derived from Einsteines E = mc2 and Planck es E = hf.

E = mc2 = hf

hc/λ = mc2

λ = h/mc ihere λ is iavelength of yartcle m), m is mass Kg), mc is momentum of the yartcles Ns

or Kgms-1)

LHS λ iave yroyertes, RHS mc momentum yartcle yroyerty

λ = h/mv

The iave-yartcle duality is not limited to yhotons. De Broglie believed yartcles has yroyertes

similar to iaves and reylaced c iith v of any yartcle. Any yartcle iith momentum can have a

iavelength and behave lik e a iave mater iave). The iavelength of any yartcle iith mv can be

found. Wavelengths formed by large 1k g<) have very small iavelengths that are unable to be

iitnessed iith human vision.

Evidence

Davisson and iermer studied the surface of Nick el crystal by observing the scatering of electrons

Nick el crystal acts as a diiracton gratng unelyectedly due to anneal) electrons gave diiracton

yatern similar to X-Rays. Diiracton have been seen iith neutrons, He and alyha ihere λ matches

de Brogliees yredictons.

As angle θ ias changed, a diiracton yatern ias made. Diiracton is a iave yroyerty. Wavelengths

measured from electron diiracton interference yaterns matched De Brogliees λ = h/mv)

yredictons, confrming his mater-iave theory. ieorge Thomson fred a beam of electrons through

a thin gold foil and observed diiracton rings thus, 2 teams using diierent elyeriments, yroved the

iave nature of electrons thus, yroving De Brogliees yroyosal.

Ligat Electron

Wave Younges double slit elyeriment Electron diiracton

Partcle Photoelectric eiect Electron acceleraton in cathode ray tube yaddle iheel, defecton)

Ayylying mater iaves to the electrons of an atom:

Quantsed energy levels of the H atom

Bohres yostulate electrons move in integer orbits) around the nucleus iithout radiatng energy. This

observed stability Bohr ias unable to elylain. De Brogliees mater iaves elylained the stability of

electrons i.e. electrons moving in standing iaves round nucleus, electron is on iave. +f an electron

sets uy a standing iave around the nucleus, the circumference is 2πr and there are a ihole number

of iavelengths number contained deyends on circumference of orbital).

nλ = 2πr sub de Broglie λ = h/mv) nh/mv = 2πr mvr = nh/2π thus, angular momentum is

quantsed)

Bohres fourth yostulate for angular momentum L is quantsed) thus, confrming de Brogliees mater-

iave.

Hoi does the standing iave become an orbitald

The tio ends are connected. Standing iave allois energy to be quantsed, stability due to Bohres

fourth yostulate. +n a standing iave there is no acceleraton thus, no EMR.

Schrodingeres contributon to the model

(rom the 1920s, modern quantum mechanics ias develoyed by Niels Bohr, Louis de Broglie, Werner

Heisenberg and Eriin Schrodinger.

(rom 1925 Schrodinger made a signifcant contributon using de Brogliees mater iave yroyertes to

yroduce the frst full quantum model of the atom.

(igure 6 ireen shois oscillaton

HΨ = EΨ ihere Ψ is iave functon that tells locaton of the yartcle, E is yartcle energy, H is

Hamiltonian that is a constant) shois hoi electrons reside in an electron cloud

Schrodingeres model overcame most of the

limitatons of Bohres model and formed the basis

of our current model of the atom. Schrodingeres

iave equaton^ gives the yositon of the

electrons as yrobability clouds rather than in a

circular orbit.

Syecial relatvity, Heisenberges uncertainty yrinciyle on the quantum level, k noiing the yositon of

the yartcle, the momentum iill be unk noin as the yartcle has been disturbed by the detecton

device), Paulies elclusion yrinciyle no tio electrons in an atom iill have elactly the same quantum

numbers i.e. electron syin ms), angular momentum l), magnetc moment m, the induced magnetc

feld of electrones orbital movement), orbital number n)) into Schrodingeres model ihich elylains

hoi so many electrons can be located closely in clouds as the elclusion yrinciyle means no tio

electrons are going to comyletely reyel almost all quantum numbers are directon, only n is a

number)

Model is imyerfect not agreed on interyretaton on iave functon, ihat is iavingd). Allois us to

fnd yrobability of fnding an electron in an orbital.

Proyertes of the Nucleus

Syontaneous Decay of Unstable Nuclei and the Proyertes of alyha, beta and gamma.

Nucleons – ihates inside the nucleus, yrotons and neutrons. Negatve electrons surround the

nucleus.

Atomic number z number) – number of yrotons in the nucleus = electrons in neutral atom

Mass number A) – number of yrotons + neutrons nucleons)

+sotoyes of an element have the same number of yrotons, but diierent number of neutrons.

+sotoyes are chemically identcal but, have diierent yhysical yroyertes. A radio-isotoye is unstable

and emits yartcles α 42H) and β e-) untl they become stable. Unstable nuclei release high energy

radiaton ionising radiaton. Syontaneous decay is a loss of mass ∆m = mass defect) as some

mass is converted into energy E = mc2) eg: α 42H) and β e-) decay. This changes a radio-isotoye into

a diierent element transmutaton). γ radiaton high energy EMR) is also emited from unstable

nuclei

The /4 tyyes of radioactve decay:

Alyha Payer Helium nucleus 2 yrotons, 2 neutrons)Travel at 0.1c and have a +2 charge

Minus 4 from atomic mass, minus 2 from atomic number

Elamyle:Uranium Thorium{¿¿238 ¿92¿ {¿¿U→{¿¿234¿90 ¿{¿¿Th+{¿¿ 4¿2 ¿{¿¿He

Relatvely heavy

Beta - occurs if nucleus has too many neutrons)

Aluminium foil ElectronTravel at 0.9cHave -1 chargeLighter than alyha yartcles

No change to atomic mass, addone to atomic number becauseneutron decays to yroton). As neutron is slightly heavier,

the e- and ¿ {v } ant-neutrino) are emited

Elamyle:¿

Beta + occurs if nucleus has too many yrotons, yroton decays toneutron)

Aluminium foil PositronTravel at 0.9cHave +1 chargeLighter than alyha yartcles

No change to atomic mass, minus one to atomic number because neutron decays to yroton). As neutron is slightly heavier, the e- and v neutrino) are emited

Elamyle:¿

iamma Concrete High energy EMRTravel at cNeutral

No change

Used

PET yositron emission tomograyhy)

The yatent is given a yositron emiter Olygen-15) that goes into tssue and interacts iith electrons to

yroduce gamma rays thus, image of tssue is cayture on comyuter.

Analyse:

8.4.2 Half-Life

The actvity of a radioactve isotoye is measured using half-lives t½). Half-life: tme for nuclei to undergo

decay untl half of its original mass is retained. (or elamyle: Polonium 2 8 has a half-life of min

therefore, afer min half of the original radio-isotoye remains. As tme yrogresses a smaller and smaller

amount of the original radio-isotoye remains.

The number of yartcles remaining is found using: Nt = Noe-λt ihere Nt is number of radioactve nuclei

remining at tme t, no is startng number of nuclei, t is tme yeriod for one half-life, e is the e constant

λ = ln2/t½ ihere t½ is half-life, λ is decay constant units of tme given)

n = t/t½ NOT ON (ORMULA SHEET

A = A0 1/2)n NOT ON (ORMULA SHEET

The actvity is the number of decays yer second that occurs in a samyle of radioactve material. +t is

measured in becquerel Bq) ihere 1 Bq = 1 decay yer second

Curve of number of nuclides remaining vs number of half-life is an elyonental decay curve of Noe-λt

(inding decay constant:

λ = ln2/t½ or n = t/t½

8.4. Nuclear (ission Controlled eg: nuclear reactor in a yoier ylant

Name and defne: Nuclear fssion occur ihen an atom sylits into tio lighter nuclei atom), mass is

converted into energy E = mc2) heat). Nuclear fssion reactors release energy at a controlled rate

thermal reactor). Neutrons incite fssion. Nuclear fssion: ihen a heavy atom is bombarded iith

neutrons, U-2 5 absorbs one neutron ihich forms a highly unstable comyound nucleus ihich sylits

into tio ayyrolimately equal elements and releases neutrons.

What is a nuclear reactor comyosed ofd

1. (uel core – nuclear fuel contains fssionable material materials that can sylit uyon absorbing

a neutron) i.e. Uranium is made uy of isotoyes, 99% is U-2 8, 0.7% is U-235, 0.006% is U-

2 4. Only U-2 5 is fssionable yelloi cak e) as it undergoes fssion immediately ihereas U-

2 8 is fertle material since it can be converted by neutron cayture that causes decay to

Plutonium-2 9 before sylitting thus, non-fssionable. Most reactor fuel is a milture of U-2 5

and U-2 8.

2. Moderator – Neutrons released by a chain reacton (ission reacton, eg: U to Kryyton and

Barium, Caesium and Rubidium or Lanthanum and Bromine) need to be sloied doin.

Sloier neutrons interact more efciently iith a U-2 5 atom i.e. increases chances of fssion

iith sloier neutrons. This is done so by imyeding their elit yathiay and alloiing neutrons

to collide iith atoms that donet absorb neutrons moderator) iater, grayhite or heavy

iater)

. Control rods – the chain reacton can be controlled by loiering control rods that absorb

neutrons in the reactor core, usually steel containing Boron/Cadmium ihich cayture

neutrons i/o undergoing fssion. Removing the control rods from the reactor allois for an

increase in rate of fssion. Loiering control rods into reactor core, loiers fssion rate.

4. Coolant - most of the energy in fssion reactons are carried aiay by the fssion yroducts

Barium, Kryyton, neutrons) ihich collide iith the coolant iater, helium – some can also

be the moderator) and yroduces heat. The coolant removes heat.

a. Primary coolant – never leaves the reactor and is highly radioactve

b. Secondary Coolant – eg: iater from a nearby natural source through a heat

elchange yrocess, heat is removed from the yrimary coolant and the secondary

coolant turns to steam ihich syins a turbine to produce electricity waica is tae

point of tae reactor. Held in a cooling yond before being returned to the reactor or

released back to iater source once temyerature is back to 20-25oC

5. Radiaton Biological Shield – to refect neutrons back to into the centre and the yrotect ialls

of the reactor from radiaton. Made from high density concrete, 2- m thick .

Controlled Fission has a 1:1 rato to yrevent a runaiay reacton

Uncontrolled fssion reacton (nuclear bomb)

Each released neutron is alloied to induce fssion in three other uranium-2 5 atoms. There is an

elyonental build uy of atoms undergoing fssion leading to a runaiay elylosion large release of

energy). Requirements:

Enriched fuel 100% U-2 5

No control rods

No moderator

No coolant

No shield

Elamyle of Uranium fssion:

23592U+

10n→236

92U→141

56Ba+92

36Kr+3 1

0n

8.4.5 Nuclear Fusion

Name and defne: As in alyha, beta, fssion and fusion reactons the atomic number Z) and mass

number A) on both sides of the equaton sum uy to equal each other conserved). Mass number

and charge are confused.

21H+

21H→3

1H+

11H+4.03MeV

Nuclear fusion is the combining of smaller nuclei to form heavier nuclei, eltremely high

temyeratures are required. A small amount of mass is lost during fusion as energy binding energy).

Nuclei are yositvely charged no electrons) and reyel due to electrostatc forces. +n fusion reactons,

ayyroaching nuclei must have enough syeed to overcome the electrostatc reyulsion forces to get

close enough for the strong nuclear force to tak e eiect. The energy barrier is the energy required to

overcome the electrostatc reyulsion force loier than energy released yer nucleon in fusion).

Energy released in fusion is greater than fssion, iith no radioactve iaste, no yolluton eg: Natonal

+gniton (acility.

Nuclear transmutaton is the yrocess of one element changing into another element through nuclear

reactons.

Natural transmutaton is ihen radioactve isotoyes syontaneously decay over a yeriod of tme and

transform into other more stable isotoyes.

Artfcial transmutaton occurs ihen a nuclear reacton is triggered by one of the reactants.

8.4.6 Energy from Nuclear Reactons

Name and defne: mass of a nucleus A) is aliays less than the sum of the mass of its individual

nucleons eg: tio seyarate yrotons and tio seyarate neutrons iill have slightly greater mass than a

42He nucleus. The mass of the atom is less than the sum of the masses of its comyonents yrotons,

neutrons, electrons).The mass of the nucleus is less than the sum of the masses of its comyonents

yrotons, neutron)

Describe: the large energy involved in nuclear reactons fssion and fusion is due to Einsteines E = mc2

Mass defect = consttuent nucleons – mass of nucleus A)

∆m = mass of yrotons, neutrons, electrons – atomic mass

Convert to AU

Mass MUST in k g for E = mc2 . Binding energy yer nucleon

(ind mass defect of U–2 5

92 yrotons l 1.007224 = 92.66465984

92 electrons l 0.000548 = 0.05045

14 neutrons l 1.008429 = 144.205298

Mass defect = 2 6.9204 – 2 5.04 9 = 1.87648084

E = mc2

= 1.876480 l 1.661 l 10-27 l l 108)2

= …

Binding energy yer nucleon:

Mass defect l 9 1.5 MeV data sheet)

= 1747.8 MeV in one nucleus)

= 7.4 8 MeV yer nucleon divided by no. of yrotons and neutrons, mass number)

Binding Energy

Binding energy is defned as the energy needed to seyarate the atom into its consttuent yarts.

During nuclear reacton fusion and fssion) the yrinciyle of LCE ayylies. When atoms lose some of

their original mass mass defect) due to the LCE the lost mass is converted to energy E = mc2). The

energy released yer nucleon is greater during fusion reactons.

Trends from a BE grayh are:

Binding energy of nucleon increase as the smaller nuclei fuse together, this is the energy

released during fusion

Elements i/ A = 40-80 have the most stable nuclei, they have the highest binding energy yer

nucleon and tak e more energy to break nuclei ayart.

(ission is everything afer iron

Larger nuclei greater than iron) have a loier binding energy yer nucleon relatvely loier

stability

+ron 56) has the most stable nucleus. Nuclei smaller than iron undergo fusion and release

energy. Nuclei larger than iron undergo fssion and release

energy.

(or small atom Z < 20), N: Z = 1 for

nucleus to be stable

(or large atoms, stable nuclei have

neutron-to yroton ratos near 1.5:1. This

is because a larger number of neutrons

is needed to stabilise the strong

reyulsion amongst yrotons.

Alyha decay

Belt of stability

N:Z = 1:1

No stable isotoyes afer

Z = 20

Unstable if out of belt

of stability

Unstable nucleus ihen

neutrons 126+

Unstable nucleus ihen

yrotons 82+

Beta decay

Deey +nside the Atom

Are Protons and Neutrons (undamental Partclesd

(undamental yartcles are elementary, indivisible yartcles

The model of the atom that ie use today has a nucleus yositve yrotons and neutral neutrons

surrounded by a cloud of negatve electrons. A fourth yartcle, the yhoton has no mass and no

charge but has quantsed energy and momentum. The electron and yhoton ayyear to be

fundamental yartcles.

Elyerimental evidence suggests the neutron has its oin magnetc feld indicatng the neutron has

internal structure and contains charges that cancel out 0 net charge) Therefore the neutron is not a

fundamental yartcle.

Evidence of radioactvity yositron emission/beta+) a yroton transmutes into a neutron iith the

emission of a yositron and a neutrino suggested that the neutron and yroton are not fundamental.

Cosmic ray elyeriments led to discovery of nei yartcles of muons and mesons.

Cloud chamber elyeriments iith cosmic rays allois for detecton of yositrons and ionising radiaton

alyha beta).

8.5.2 Standard Model of Mater

Mater – molecule atom

Proton and neutrons quark s

Lepton (ermion), 6 tyyes Electrons, muons, neutrino, tau. Do not elyerience the strong force, so they cannot be held in a nucleus.

MaterQuarks (ermion) 6 tyyes grouyed in yairs [uy-doin 1st mak e yroton, neutron), strange-charm 2nd, toy-botom rd detectable)] Bosons

Massless and mediate force eg: Photon, gluon, Higgs Boson, Z boson, W boson

Hadronscomyosite yartcle made of quark s aliays have integer charge)

Baryon quark s/ant-quark s comyosite eg: yroton, neutrons

Mesonquark and antquark eg: yion, eta, meson, Kaon

(undamental yartcles, indivisible, no k noin smaller comyonents

Positron

emission/electron

cayture

The atom consists of neutrons, electrons and yrotons. Partcle accelerators and nuclear reactors

have revealed other subatomic yartcles such as quark s, neutrino v), ant-neutrino, yositron. The

standard model atemyts to describe all interactons of subatomic yartcles and ylaces mater into

grouys. All yartcles have antyartcles oyyosite charge, identcal otheriise)

Formula of proton:

UUD = + 2/ e + 2/ e - 1/ e = +1e

Formula of neutron:

UDD = +2/ e - 1/ e – 1/ e = 0 = neutral charge

4 fundamental forces in the universe ihich act by elchanging force yartcles boson): ieak est to

strongest – gravity [acts through graviton elchange yartcle not yet discovered)], electromagnetc

force [acts through yhotons], ieak nuclear force [acts through z and i bosons], strong nuclear force

[through gluons shoi using squiggly lines)]

Discovery of tae Higgs Boson

Peter Higgs yredicted the Higgs Boson in 1964 ihich ias detected using ATLAS at CERN in the large

hadron collider in 2012 Nobel yrize 201 ). This confrms the standard model. Bosons are force

mediatng yartcles or elchange yartcles

Boson force elchange yartcles

As electron A ayyroaches electron B, each electron emits a yhoton that is absorbed by the other

leading to an elyerience of a force of reyulsion or atracton, yhoton is resyonsible for this.

(orce yartcles cause atracton forces betieen mater by being elchanged in such a iay that the

mater yartcles are yushed toiards each other. Reyulsion forces occur by having force yartcles

elchanged in such a iay that the mater yartcles are yushed aiay from each other.

Weak nuclear forces are resyonsible for nuclear decay alyha and beta) and contributes minuscule to

k eeying atom together * allois for yartcle to be emited

iravity - graviton

Electromagnetsm – yhoton

o Range of eiect is infnite since it has no rest mass

o Elyerienced by everything iith charge quark s, leytons, �±)

o Holds atoms and molecules together through the atracton betieen the nucleus

and the electrons, and the atracton betieen atoms in a molecule

Strong nuclear force - gluon

o Resyonsible for k eeying the nucleus stable and together

o Diminishes iith increasing seyaraton and is negligible for seyaratons greater than

about 10-14m.

o iluons can only have an eiect over a very short range.

Weak nuclear force – Z W boson

o Elyerience by quark s and leytons

o Resyonsible for nuclear radiaton and fssion

o Only force that can change the favour tyye) of a quark or leyton. +t allois quark s

and leytons

o The ieak force is the only force that can change the charge of a yartcle, because

�+, �−are the only charged force carriers.

o The most common elamyle of a ieak interacton is beta decay. Beta-minus decay is

due to the ieak force turning a doin quark into an uy quark , hence a neutron into

a yroton.

o

(irst generaton yartcles form mater. Second generaton yartcles are less stable and decay to form

1st generaton yartcles. rd generaton yartcles are even more unstable and decay to form 2nd

generaton. 2nd and rd generaton yartcles cannot mak e uy mater and are harder to detect. As

generaton increases, mass of yartcle also increases.

+s the standard model comyleted

Has been eiectve in yredictng elyerimental results eg: gluon, Higgs Boson, W and Z Bosons, 6

quark s have all been elyerimentally confrmed. Hoiever, the standard model is stll incomylete

because it claims neutrinos have 0 mass, does not include the gravitatonal force graviton), dark

mater or dark energy. Testng the limits of the standard model elyerimentally are areas of ongoing

research at LHC. Physicists hoye to develoy the grand unifed theory that iould incoryorate dark

mater and energy.

Partcle Accelerators

Most of standard model ias verifed using yartcle accelerators.

1. Partcles are accelerated to near the syeed of light, giving them much higher energy than

they iould ordinarily have.

2. The high-energy yartcles are made to collide

. The k inetc energy is converted to rest mass, creatng nei yartcles that can be studied

With more yoierful yartcle-accelerators that can yroduce yartcle collisions increase in

subatomic yartcles discovered eg: Large Hadron Collider LHC). Partcle accelerators give yrotons,

electrons or ions charged yartcles) must have a charge) enough energy to smash into one another.

Elamyles of yartcle accelerators:

19 0s Van de iraaf ienerator – Devised a contnuous high voltage suyyly that could be used to

accelerate and ions to energies of 0.5MeV canet measure syeed very iell so use energy to

reyresent syeed).

1960s Linear accelerators – Eg: Stanford Linear Accelerator Centre SLAC) ihere charged yartcles

are yassed through a k m evacuated tube, electrons accelerator accelerated to 50ieV very close to

c). Pioneered the discovery of yrotons as non-fundamental yartcles through deey inelastc

scatering:

- Electrons and yrotons are fred at each other at high syeed

- At loier energies, the electron and yroton elastcally scater

- At high energies, the yroton absorbs some energy from the electron ihich mak es the

collision inelastc. The yroton is then able to emit a quark .

- Scatered if as they iere dense yositve charges in a yroton. +t ias not lik e billiard

- balls

- +f the yroton is able to absorb energy and emit a yartcle, it cannot be a fundamental yartcle

Cyclotrons – charged yartcles move through semi-circular arcs. As their velocity increases, so does

the radius of the arc DONeT P+CTURE A SP+RAL, MORE L+KE ELCTRON SHELLS. Toiards the outside of

the last arc, the yartcle is defected toiards the target. All charged yartcles.

- A small tube leads a stream of hydrogen gas to the centre of the bol ihere a syark striys

aiay the electron from each atom.

- An alternatng electric feld betieen the gay accelerates the yroton ihen yassing across the

gay.

- The magnetc feld steers the yroton into a circular traedectory. The magnetc feld directon is

yeryendicular to the ylane of the circle.

- As the yrotons accelerate in a circular traedectory, they yass cross the gay betieen the tio

coyyer ‘Des.

- As the yrotons gain energy, the radius of their orbit increases and they gradually syiral out

to the limit of the magnetc yolees area. Air is removed from the entre region so that

collisions iith air molecules do not interfere iith the accelerator.

Betatron – accelerates electrons but in system lik e Cyclotron

Synchrotron – main accelerators in contemyorary use eg: LHC. Stll uses a circular yath but the

yartcles are k eyt in a constant radius by using suyer conductng magnets thus, shaye is a ring rather

than a disk . The B feld can be concentrated on yortons of the yartcle rather than full area.

+n a synchrotron, the yath travelled is a circle, hoiever the frequency of the electric feld and

strength of the magnetc feld has to change deyending on the velocity of the yartcle.

- The electric and magnetc felds have to be synchronised to the yositon and velocity of the

yartcles

The Large Hadron Collider is an enormous collider. +t uses a linear accelerator to initally accelerate

the yartcles, then a series of synchrotrons to accelerate the yartcles in stages.

+t ias built afer yrevious results from accelerators hinted at the elistence of the Higgs boson, the

yartcle that is hyyothesized to give yartcles their mass. +n 2012, the LHC detected a yartcle that

behaved lik e a Higgs boson.

Elylain: role of yartcle accelerators in obtaining evidence that tests or validates the Standard Model

and other theories.

Partcle accelerators assist in yrobing and investgatng the structure of mater by:

High energy high syeed λ = h/mv iavelength reduces as v increases smaller iavelengths

results in higher resoluton alloiing very small yartcles to be detected

High energy higher mass/momentum can be detected as it is larger Pv = m0v/√1-v2/c2

A vast maedority of yartcles can only be observed in high energy yartcle accelerators, at loier

energies these yartcles are not visible

Work ing Scientfcally:

Reliability

Reliability is the eltent of ihich an

elyeriment yields consistent

results

To alloi a yerson to determine

the reliability of an elyerimentes results, the elyeriment must be reyeated + tmes

Presence of random errors in the elyeriment reduce reliability but, systematc errors have

no imyact

A set of results can be inaccurate but, reliable

An elyeriment is reliable if reyetto of the elyeriment yields the same results. A measurement is

reliable is ihen reyeated there is a similar result.

Reducing imyact of random errors on the method imyroves reliability. Removing outliers, reyeatng

the elyeriment and averaging results hely yield imyroved reliability.

Validity

Does the elyeriment test the hyyothesis + iantd Have all variables been k eyt constant

besides the indeyendent and deyendent variabled

Eltent of ihich the elyeriment tests the hyyothesis and addresses elyerimental aim

control variables adequately controlled, only one +V and DV).

Deyendent on suitability of elyerimental design and yresence of systematc errors.

Method must satsfy all assumytons.

Accuracy

Eltent of ihich elyerimental results match iith the true and acceyted value. Can be increased

through reducton of systematc errors. Can be tested by comyaring elyerimental value to acceyted

value.

The accuracy of a measurement is a iay of talk ing about the total error in your fnal result. An

accurate measurement is very close to the true value. Just because a measurement is accurate

doesnet mean it is yrecise an accurate value iith a iide yossible range isnet very useful.

Percent error: acceyted value-elyerimental value/acceyted value) l 100

Error: (referring to degree of accuracy)

Systematc

Biases measurements in some yredictable iay, although you may not k noi hoi to yredict

it. +t either increases or decreases the measurement consistently. A simyle elamyle iould

be a voltmeter that only disylays 90% of the true voltage, so the size of the error changes

deyending on ihat youere measuring. No imyact on reliability.

Random

A random error is an error that is yresent every tme you tak e the measurement, but ihich

varies unyredictably in size and directon. Random errors are aliays yresent. The eiects of

random errors can be reduced only by reyeatng the measurement many tmes.

Illegitmate

An illegitmate error is a one-tme mistak e in the yrocedure that yroduces a bizarre value. +f

you k noi you made a mistak e then you can edust throi out that measurement. Usually the

mistak e is more subtle, for elamyle misreading a disylay or an unelyected yoier surge in

the equiyment. +n this case some statstcal criteria is used to throi out data that

are iell outside the normal range of yossibility outlier).

Uncertainty (refer to degree of precision and accuracy)

Absolute uncertainty: 0.5 l limit of reading for analogous scales and limit of reading for digital

scales, or largest deviaton from mean

Relatve Uncertainty: elyresses relatve size of uncertainty of measurement. Absolute

uncertainty/value) l 100

When multyle readings are tak en to reduce the eiect of random error, the uncertainty is

determined by fnding the average value and then comyaring the average to the readings. The

greatest variaton iithin the readings from the average becomes the uncertainty unless this is less

than the uncertainty of the readings themselves). This can be elyressed as an absolute error or

relatve error.

Signifcant fgures are sometmes used as an imylicit iay of indicatng uncertainty. When this occurs,

the last digit is considered uncertain. (or elamyle, a result reyorted as 1.2 imylies a minimum

uncertainty of ±0.01 and a range of 1.22 to 1.24.

Uncertainty in tae measurand (dependant variable):

Range is malimum – minimum value)

Value of measurand = average value of multyle measurements or minimum value + 0.5 range

Uncertainty in this is 0.5 range = 0.5 mal – min)

Uncertainty should only be reyorted to one or tio signifcant fgures.

Uncertainty of the average:

1. (ind range of values mal – min)

2. Divide range by 2, this is the uncertainty.

. Uncertainty of the average is R/2√N, ihere R is range and N is number of values

Precision: elyresses amount of confdence in the reyroducibility of measurements reliabilityd).

More decimal ylaces on measurement tool indicates higher yrecision. The yrecision of a

measurement is the total amount of random error yresent. A very yrecise measurement has small

random errors i.e. a small syread of results, but edust because a measurement is yrecise doesnet mean

that it is accurate see beloi) undiscovered systematc errors might sk ei your results drastcally.

The yrecision of the fnal result of an elyeriment cannot be beter than the yrecision of the

measurements made during the elyeriment, so the aim of the elyerimenter should be to mak e the

estmates as good as yossible. Reyeatability of measurement of a value.

Uncertainty Calculaton Rules:

1. +f a measured quantty is multylied/divided by constant then the absolute uncertainty is

divided/multylied by same constant relatve stays the same)

2. +f 2 measured quanttes are added or subtracted then absolute uncertaintes are added

. +f more than tio measured quanttes are multylied/divided then relatve uncertaintes are

added

4. +f quantty is raised to a yoier then relatve uncertainty is multylied by the yoier

Rounding:

When the digit to be droyyed is less than fve, irite the number iithout the last digit. e.g. 105.874

becomes 105.87

When the digit to be droyyed is greater than fve, the yreceding digit is increased by one. e.g.

105.876 becomes 105.88

When the digit to be droyyed is elactly fve, then the nearest even number is used for the yreceding

digit. e.g. 105.885 becomes 105.88 and 105.875 becomes 105.88

8.4.4

Why angular momentum quantsed evidenced

Only yredict yrobability

When discovered yrotonsd

References

HW

We need to inducton coil as ie need as higher voltage to heat uy cathode

Neutron + yrotons is toy number

Protons is botom number

CAV+TY RESONANCE

Pg 114, thought elyeriments

D = 1?

shortening blue shif, nebulae ayyroaching Earth) and

ias studying nebulae iith hook telescoye at the Hubble Observatory.

REWR+TE

Big crunch

Old star and bb notes

8min for sunlight to reach earth

Momentum increases and yartcle slois doin, natural break is 99.9999%c

Write elamyle elyeriments for centyetal

UV catastroyhe quora

Wiggle means AC

P means yrimary S means secondary

VyVs=NyNs

Ability of transformer to change voltage is deyendent on hoi iell changing ful is link ed betieen

the tio coils. Confguraton of the ironcore and coils is designed to increase ful link age.

+deally yoier out = yoier in but realistcally this can not be the case due to eddy currents. Poier

out deyends on load that is ayylied to secondary circuit. Poier in is determined by yoier out.

Shaded yoles cause change in ful through mak ing feld lines iiggly varying B feld. This is through

interacton of B feld generated by coyyer shades iith B feld of the stator yole terminals)

(lul of strays iill oyyose main ful

At mal current there is no emf thus no iarying of feld choiing change in B ful.

Shading/block ing the magnetc feld

yhase more uniform B feld and yrovide enough yoier

AC single motor back EM( trend unlik e DC motord

Mechanism of shaded yole and benefts

Why 2 namesd

Learn to drai brush dc motor.

Cathode ray tube

North to south feld lines

Uncertainty

Systematc

Random

+llegitmate

Precision

Accuracy

Absolute uncertainty

Relatve uncertainty

When reading oi a scale the uncertainty is ofen half the limit of reading

Measurements it is the last decimal ylace or the iriten decimal ylace

Signifcant fgures shoi yrecision

Non-zero digits are aliays signifcant. Any zeros betieen tio signifcant digits are signifcant. A fnal

zero or trailing zeros in the decimal yorton ONLY are signifcant.

(or additon and subtracton iriten ansier should have the least number of ylaces in the decimal

yorton of the number in the yroblem.

(or multylicaton and division the number of signifcant digits in the ansier is same number of

signifcant fgures as the number iith the feiest signifcant fgures in the data used in the

calculaton.

156000 is ambiguous, tak e the conservatve road of signifcant fgures

Rules:

5. +f a measured quantty is multylied/divided by constant then absolute uncertainty is

divided/multylied by same constant

6. +f 2 measured quanttes are added or subtracted then absolute uncertaintes are added

7. +f over tio measured quanttes are multylied/divided then relatve uncertaintes are added

8. +f quantty is raised to a yoier then relatve uncertainty is multylied by the yoierd