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1



Contents1.0 Kinematics...........................................................................................10

Formulas.............................................................................................102.0 Force....................................................................................................10

Tension...................................................................................................10

The Normal Force and Friction................................................................11

Drag Force..............................................................................................11

Formulas.............................................................................................12

4.0 Statics.................................................................................................12

4.2 Equilibrium.......................................................................................12

4.3 Torque..............................................................................................12

4.4 rinci!le o" #oments........................................................................12

4.4 $entre o" %ra&it'($entre o" #ass.....................................................12

4.) Stabilit'............................................................................................13

Formulas.............................................................................................13

*.0 Energ'.................................................................................................13

*.3 +or,.................................................................................................13

*.4 Kinetic Energ'..................................................................................14

*.* otential Energ'...............................................................................14

%ra&itational otential Energ'............................................................14

*.) $onser&ati&e Forces.........................................................................14

*.- $onser&ation o" Total Energ'............................................................14

*. o/er...............................................................................................14

#echanical Ecienc'..........................................................................14

Formulas.............................................................................................1*

-.0 Sim!le armonic #otion.......................................................................0

-.2 oo,es a/.......................................................................................0

Energ' in oo,es a/ De"ormation.....................................................0

-.3 Sim!le armonic #otion....................................................................0

elationshi! 5et/een $ircular #otion and Sim!le armonic #otion....1

2



#a6imum 7elocit' in S#.....................................................................1

eriod and Frequenc' o" S#................................................................1

-.4 The Sim!le endulum.........................................................................1

.0 +a&es....................................................................................................2.2 S# and +a&es..................................................................................2

.3 Frequenc'8 +a&elength and S!eed....................................................2

.* T'!es o" +a&es...................................................................................2

.10 +a&es and Energ'............................................................................2

Energ'...................................................................................................2

o/er and 9ntensit'...............................................................................2

.11 $om!le6 +a&e"orms........................................................................2

#usical and 7ocal Tone.........................................................................2

:.0 Sound and earing................................................................................3

:.2 Sound +a&es in #edia.......................................................................3

ressure +a&es in %ases.......................................................................3

+a&es in Solids and iquids..................................................................3

+a&e S!eed..........................................................................................3

:.3 itch and oudness............................................................................3

Frequenc' and itch..............................................................................3

;m!litude and 9ntensit'........................................................................4

9ntensit'8 oudness and the decibel scale.............................................4

:.4 esonance and Sound %eneration.....................................................4

The uman 7ocal $ords........................................................................4

:.* The Ear...............................................................................................4

;natom'................................................................................................4

The Ear and the !roblem o" im!edance................................................*

:.) The Do!!ler E<ect.............................................................................*

10.0 Elasticit'= Stress and Strain.................................................................)

10.2 Tension and $om!ression.................................................................)

Tensile Stress and Strain.......................................................................)

$om!ressi&e Stress and Strain.............................................................-

3



10.* Elasticit'...........................................................................................

Stress>Strain $ur&es..............................................................................

11.0 ressure...............................................................................................:

11.3 ressure...........................................................................................:Solids....................................................................................................:

%ases....................................................................................................:

iquids...................................................................................................:

11.3 Densit'.............................................................................................:

11.4 ascals rinci!le.............................................................................10

12.0 5uo'anc'...........................................................................................11

12.2 The 5uo'ant Force.........................................................................11

;rchimedes rinci!le..........................................................................11

14.0 Fluid D'namics o" Non>7iscous Fluids...............................................12

14.2 De?nition o" Ke' Terms...................................................................12

14.3 The equation o" $ontinuit'.............................................................12

7olume Flo/ ate................................................................................12

$ontinuit' o" Flo/...............................................................................12

14.4 5ernoullis Equation.......................................................................12

5ernoullis rinci!le and 9ncom!ressible Fluid Flo/............................12

Energ' Densit'....................................................................................13

ressure and 7elocit'..........................................................................13

;!!lications o" 5ernoullis Equation....................................................13

1*.0 Fluid D'namics o" 7iscous Fluids.......................................................1*

1*.2 7iscosit'.........................................................................................1*

oiseuilles a/....................................................................................1*

Ke' $once!ts..........................................................................................1*

1-.0 Tem!erature and the @eroth a/......................................................1-

1-.2 Thermal Equilibrium.......................................................................1-

1:.0 hase and Tem!erature $hange........................................................1

1:.2 hase $hange................................................................................1

hase Diagrams..................................................................................1

4



hase $hanges and atent eat.........................................................1

1:.3 Tem!erature $hanges....................................................................1:

eat and Tem!erature........................................................................1:

S!eci?c eat.......................................................................................1:1:.4 Energ' $onser&ation......................................................................20

The Sim!le $ase > No hase $hange..................................................20

Thermal Equilibrium /ith hase $hange.............................................20

21.0 eat Trans"er.....................................................................................21

eat Trans"er b' $onduction...............................................................21

$oecient o" eat Trans"er.................................................................21

$onduction Through #ulti!le a'ers...................................................21

21.3 $on&ection.....................................................................................21

21.4 adiation........................................................................................21

The Ste"an>5oltAmann a/.................................................................22

$olour and Tem!erature......................................................................22

21.* $ombined Trans"er rocess............................................................22

22.0 Thermod'namics and the 5od'.........................................................24

22.2 The First a/..................................................................................24

22.4 Energ' and the 5od'......................................................................24

#etabolism8 '!othermia and '!erthermia.....................................24

Ecienc'.............................................................................................24

23.0 Static Electricit'................................................................................2)

23.2 $harge............................................................................................2)

23.3 $onductors and 9nsulators.............................................................2)

Ke' $once!ts..........................................................................................2)

24. 0 Electric Force Field and Electric Field................................................2

24.1 9ntroduction....................................................................................2

24.2 $oulombs a/...............................................................................2

24.3 Su!er!osition o" Electric Forces.....................................................2

24.4 9n&erse Square a/........................................................................2

24.* The Electric Field............................................................................2

*



24.) Electric Field Diagrams...................................................................2:

24.- Su!er!osition o" Electric Fields......................................................31

Ke' $once!ts..........................................................................................31

2*.0 Electrical otential and Energ'..........................................................322*.2 Electrical otential Energ'..............................................................32

2*.3 Electrical otential..........................................................................32

23.4 Electrical otential and +or,..........................................................32

24.- The eart and E$.........................................................................33

Ke' $once!ts..........................................................................................34

2).0 $a!acitance.......................................................................................3*

2).1 9ntroduction....................................................................................3*

2).2 The $a!acitor.................................................................................3*

2).3 Energ' Stored in a $a!acitor..........................................................3)

Ke' $once!ts..........................................................................................3)

2-.0 Direct $urrents and D$ $ircuits.........................................................3-

2-.1 9ntroduction....................................................................................3-

2-.2 Electric $urrent..............................................................................3-

2-.3 $urrent Flo/ and Dri"t 7elocit'.......................................................3-

2-.4 Direct &ersus ;lternating $urrent...................................................3

2-.* $ircuits and $ircuit Diagrams.........................................................3

2-.) o/er Sources.............................................................................3

2-.- esistance and Bhms a/............................................................3:

2-. esistors and esisti&it'.................................................................3:

2-.: +ires..............................................................................................3:

2-.10 Kircho<s a/...............................................................................40

Kircho<s a/ o" 7oltages=..................................................................40

Kircho<s a/ o" $urrents...................................................................40

2-.11 esistors in Series and arallel.....................................................40

esistors in Series...............................................................................40

esistors arallel.................................................................................40

2-.12 o/er Dissi!ation.........................................................................42

)



2-.13 ;lternati&e Energ' Cnits..............................................................42

2-.14 Electric Shoc, aAards.................................................................42

2-.1* Electricit' in $ells.........................................................................43

$ell #embrane....................................................................................43$ircuit #odels o" the $ell and the $ell #embrane..............................43

Ke' $once!ts..........................................................................................44

2.0 Time beha&iour o" $ $ircuits...........................................................4)

2.2 The $ $ircuit.................................................................................4)

2.3 Discharging $ $ircuit....................................................................4)

2.4 $haring $ $ircuit..........................................................................4-

Ke' $once!ts..........................................................................................4-

2:.0 The Nature o" ight............................................................................4

2:.2 Electromagnetic +a&es..................................................................4

The constant s!eed o" light.................................................................4

+a&elength and "requenc'.................................................................4

2:.3 eection.......................................................................................4:

2:.4 e"raction.......................................................................................4:

Snells a/..........................................................................................*1

Total 9nternal eection.......................................................................*1

31.0 The E'e and 7ision............................................................................*2

31.2 The arts o" the E'e.......................................................................*2

31. ;lternati&e Structure and lacement.............................................*3

Focusing ;bilit'...................................................................................*3

E'e lacement and Field o" 7ision.......................................................*3

31.: $olour 7ision..................................................................................*3

Detector T'!es....................................................................................*3

$olour Science....................................................................................*3

33.0 ;toms and ;tomic h'sics................................................................*4

33.2 arts o" the ;tom...........................................................................*4

33.3 Brbitals and Energ' e&els.............................................................*4

Electrons.............................................................................................*4

-



Brbitals and Energ' e&els.................................................................*4

Emission and ;bsor!tion S!ectra........................................................*4

34.0 The Nucleus and Nuclear h'sics......................................................*)

34.2 Nuclei and 9soto!es........................................................................*)rotons and Neutrons..........................................................................*)

;tomic Number...................................................................................*)

S'mbols and Terminolog'...................................................................*)

34.3 Energ' and #ass Cnits...................................................................*)

Equi&alence o" #ass and Energ'.........................................................*)

The Electron 7olt.................................................................................*)

The ;tomic #ass Cnit..........................................................................*-

34.3 Nuclear Forces................................................................................*-

The Strong Force and the Nucleus......................................................*-

The +ea, Nuclear Force......................................................................*-

3*.0 roduction o" 9onising adiation........................................................*

3*.1 introduction....................................................................................*

3*.2 Nuclear Deca' rocess...................................................................*

;l!ha Deca'........................................................................................*

5eta Deca'..........................................................................................*

%amma Deca'....................................................................................*:

3*.3 ;cti&it' and al">i"e......................................................................)0

;cti&it'................................................................................................)0

al" i"e...............................................................................................)0

#ost i,el' Deca' #ode and E6am!les o" Deca' Series.....................)1

3*.4 >ra' roduction.............................................................................)1

5remsstrahlung...................................................................................)2

>ra' Tubes..........................................................................................)3

3*.* Bther Sources o" adiation............................................................)3

air ;nnihilation..................................................................................)3

Ke' $once!ts..........................................................................................)4

2).0 9nteraction o" 9onising adiation........................................................))



3).2 ;ttenuation o" >ra's and $ross Section........................................))

3).3 >ra's and %amma adiation.........................................................))

The hotoelectric E<ect......................................................................))

air roduction....................................................................................)-$om!ton E<ect...................................................................................)-

3).4 articles..........................................................................................)

Neutrons.............................................................................................)

9ons.....................................................................................................)

Electrons(ositrons..............................................................................):

3).* Detection o" 9onising adiation......................................................):

The %eiger>#ller Tube.......................................................................):

hotomulti!lier....................................................................................):

hotogra!hic Emulsion........................................................................-0

Ke' $once!ts..........................................................................................-0

3-.0 5iological E<ects o" 9onising adiation..............................................-2

3-.2 #echanisms o" $ell Damage..........................................................-2

3-.3 Dose and Dose Equi&alent.............................................................-2

;bsorbed Dose....................................................................................-2

Dose Equi&alent..................................................................................-3

3-.4 T'!es o" E<ects..............................................................................-3

3-.* #edical is,s and E<ects...............................................................-4

3-.) Cltra&iolet adiation.......................................................................-4

3.0 #edical 9maging................................................................................-*

3.2 >ra' 9maging.................................................................................-*

3.3 $T Scan..........................................................................................-*

3.4 ET Scan........................................................................................-*

3.- Cltrasound Sonogra!h'..................................................................-)

3:.0 Nuclear #agnetic esonance............................................................--

3:.3 ; brie" outline o" #9......................................................................--

:



10



1.0 Kinematics

• Velocity - change in !osition di&ided b' time it too, to occur > &ector8 has a magnitude and direction

> s!eed is the magnitude o" &elocit'• Acceleration > rate o" change o" &elocit' Gin timeH

> &ector

• Projectile motion is symmetrical about the point of

maximum height

• 2 !otion > acceleration due to gra&it' acts onl' in the &ertical

direction > horiAontal and &ertical com!onents o" &elocit' &ector are

inde!endent

"ormulas

v =∆x

∆t

a=∆ v

∆ t

v f =vi+a t

vav=d

t

v f 2−v i

2=2ax

d=v it +1

2a t

2

2.0 "orce

• #e$tons "irst %a$ > an' obIect continues at rest or at a constant

&elocit' unless an e6ternal "orce acts on it

• #e$tons &econ' %a$ > am e6ternal "orce gi&es an obIect an

acceleration. The acceleration !roduced is !ro!ortional to the "orce

a!!lied8 and the constant o" !ro!ortionalit' is the mass

• 1N is the "orce /hich /ould accelerate 1,g mass at 1m(s

• the /eight o" an obIect is a "orce not a mass

•

"orce is a &ector• #e$tons (hir' %a$ > "or e&er' action8 there is an equal and

o!!osite reaction

• Action-reaction pair)thir'-la$ force pair > each "orce in an

action>reaction !air acts on a di<erent obIect Gal/a's the caseH

• 9denti"'= contact "orces8 identi"' action>reaction !airs8 /eight "orces

and then reaction to /eight "orces

11



(ension

• e6ist in the bod' o" a e6ible cable or line

• an' "orces not directed along the cable8 result in bending o" the

cable

12



(he #ormal "orce an' "riction

• "riction force *f+ > the "orce /hich !re&ents the bloc, "rom sliding

do/n the slo!e

• #ormal "orce *#+ > !er!endicular to the sur"ace o" contact

• Critical Angle *,c+ > angle at /hich the bo6 /ill slide

• max J ma6imum coecient o" "riction

• coecients calculated "orm "rom f = µN are ,no/n as the coecient

o" ,inetic and static "riction

• the coecient o" ,inetic "riction is al/a's smaller than thecoecient o" static "riction

• normal reaction "orce o" the sur"ace is not necessaril' equal to the

/eight "orce o" the bloc,

• normal and "riction "orces are reaction "orces J the' are the result o"

action>reaction !airs bet/een atoms on the sur"ace and atoms on

the bloc,. These "orces are electrostatic in character.

rag "orce

• "orces that occur /hen solid obIects mo&e through gases and liquids

• liquid that an obIect mo&es through e6erts a "orce a!!osite to the

direction o" the obIect drag

• mo&ing through air air resistance

• magnitude o" drag "orce mo&ing through air can be modelled as

being !ro!ortional to the square o" the s!eed

• , constant !ro!ortionalit' determined b' the sha!e o" the obIect

and densit' o" air Gsee "ormulaH

13



14



"ormulas

F =m a

W =mg

f =mg sinθ

N =mgcosθ

f = N tan θ

f max= μmax N

μmax=tanθc

f (drag)=k v2

.0 &tatics

.2 /uilibrium• /hen net "orce and net torque is Aero

• static euilibrium J /hen in equilibrium and stationar'

• 'ynamic euilibrium J equilibrium and in motion Gconstant

&elocit' or constant rotational motionH

• stable euilibrium J i" it /ill return to equilibrium a"ter a small

dis!lacement

• unstable euilibrium J /ill not return to equilibrium a"ter a small

dis!lacement

. (orue

• !h'sical quantit' /hich causes an obIect to begin to rotate or mo&e

in a circle or Gmore generall'H to change its rate o" rotation

• a torque is not a "orce8 it is a moment

• scalar

• use"ul /a' to measure the e<ect o" a "orce a!!lied to a rod

• units are Nm GNe/ton metersH

. Principle of !oments

• static euilibrium J all torques are balanced8 there is no nettorque

• s'stem alread' rotating /ill not increase its rate o" rotation i" the

torques are balanced

• (he principle of moments At equilibrium, the sum of the clockwise moments will equal the

sum of the counter-clockwise moments.

1*



• !oment 3 the !roduct o" a quantit' and its !er!endicular distance

"rom a gi&en !oint

. Centre of 4ra5ity)Centre of !ass

• The centre o" gra&it' is the !oint in an obIect at /hich the "orce o"

gra&it' ma' be ta,en to act

.6 &tability

• BbIect is stable i" it /ill either remain in stable equilibrium

inde?nitel' or /ill tend to mo&e bac, to stable equilibrium /hen

dis!laced

• 9n general8 static stabilit' occurs /hen the &ertical li&e through the

obIects centre o" gra&it' !asses through its base o" su!!ort

"ormulasT = F d

∑ F cw dcw=∑ F ccw dccw

7.0 /nergy

• ;n obIect that has a certain mass and &elocit'8 is described as

ha&ing a !articular ,inetic energ'

• ;n obIect that has a certain mass and is located at a certain !oint in

a conser&ati&e "orce ?eld is described as ha&ing a !articular

!otential energ'

• Energ' is conser&ed

• The total energ' in a closed s'stem is constant o&er time

7. 8or9

• rocess b' /hich energ' is trans"erred "rom one "orm to another

• o/ much energ' has changed

•

+hat sort o" !rocess• Eg. Falling obIect gains ,inetic energ' and loses !otential energ'8

because ethe gra&itational ?eld o" the earth does /or, on the obIect

to accelerate it

• 9n the absence o" other "orces8 amount o" /or, done b' the

gra&itational "orce ?eld is the numerical increase in the ,inetic

energ' o" the obIect

• +hen a " /ith magnitude F acts on a bod'8 and it mo&es a distance

d in the direction o" the "orce8 the /or, done is W = Fd1)



• +or, is in Ioules GLH

• +hen the "orce and dis!lacement are not in the same direction8 the

/or, is calculated using the com!onent o" "orce in the direction o"

dis!lacement

1-

Fcos

Fsin

F

d



• F and d are the magnitude o" the a!!lied " and the dis!lacement

7. Kinetic /nergy

• ; measure o" the /or, that an obIect can do because it is mo&ing

• The amount o" ,inetic energ' gained b' an obIect /hich is initiall'

at rest /ill be equal to the amount o" /or, done on that obIect b' an

e6ternal "orce

7.7 Potential /nergy

• otential energ' is the energ' an obIect has because o" its !osition

4ra5itational Potential /nergy

• ; "orce must be a!!lied to the obIect to balance the do/n/ard "orce

o" gra&it' so that the obIect is able to tra&el at constant &elocit'

• This "orce is equal in magnitude to the gra&itational "orce but isdirected u!/ards

7.6 Conser5ati5e "orces

• 9m!ortant to include the ?nal and initial ,inetic and !otential energ'

• otential energ' can be con&erted into ,inetic energ' and &ice>&ersa

• Friction does not remo&e energ' but it does con&ert it into "orms

/hich de!end on the microsco!ic beha&iour o" the s'stem usuall'

treated as a dissi!ati&e "orce

• issipati5e force J remo&es mechanical energ' "orm the s'stem

under consideration

• Conser5ati5e forces J do not change the amount o" mechanical

energ' in the s'stem

• !echanical energy J ,inetic !otential energ'

7.: Conser5ation of (otal /nergy

• (he principle of conser5ation of energyThe total amount of energ in a closed sstem does not increase or

decrease. A closed sstem is one which does not e!change energ

with its surroundings

7.; Po$er

• The rate at /hich /or, is done is an im!ortant quantit'

• ate at /hich /or, is done is the !o/er

• #easured in /atts

!echanical /<ciency

• Ecienc' /or, out(/or, in /or, out!ut(energ' used

1



1:



"ormulas

W = Fd

W = Fdcosθ

KEf = KEf +W

KE=1

2m v

2

PEgravitational=mgh

P= W

∆ t

P= Fv

work ∈¿=work output

energ used

nefficienc=work out

¿

∆ KE+∆ PE=0

KE+ PE=constant

20



:.0 &imple =armonic !otion

• ;n' motion that re!eats a"ter a gi&en !eriod o" time is oscillator'

motion

:.2 =oo9e>s %a$

• &pring J the "urther 'ou stretch it8 the harder it !ulls bac,8 and &ice

&ersa

• #atural Position J the !osition the s!ring /ill sit in i" no "orce is

a!!lied Galso called equilibrium !ositonH

• "or springs J the magnitude o" the restoring "orce is !ro!ortional

to the dis!lacement o" the s!ring "rom equilibrium !osition

F =−kx

• 9 J s!ring constant

• x J dis!lacement "rom equilibrium !osition

• negati&e sign indicates the restoring "orce is al/a's to/ards

equilibrium !osition

/nergy in =oo9e>s %a$ eformation

• in order to stretch or com!ress a s!ring8 an e6ternal "orce must be

a!!lied to o&ercome the restoring "orce

• "orce increases linearl' /ith distance

• /or, done=

W =1

2 k x

2

• /or, done on a s!ring is then stored at !otential energ'8 so

there"ore=

PE=1

2 k x2

:. &imple =armonic !otion

• at equilibrium !osition8 acceleration o" a mass on a s!ring is Aero

• &elocit' o" a mass on a s!ring is greatest at equilibrium !osition

• sim!le harmonic motion GS#H J oscillation

• S# is !eriodic

22



• Each oscillation is called a cycle

• Time "or one "ull c'cle is a perio' *(+

• "reuency *f+ J number o" c'cles !er time !eriod

• Frequenc' is in =ert? *=?+ Gno. c'cles !er secondH

f =1

T

@elationship et$een Circular !otion an' &imple =armonic

!otion

• oriAontal and &ertical com!onents o" the motion o" an obIect in

circular motion at constant s!eed are e6am!les o" S#

!aximum Velocity in &=!

• Total energ' o" a s'stem undergoing S# is conser&ed• There"ore8 total energ' at an' gi&en !oint in the c'cle o" the

oscillator is Iust the !otential energ' stored in the s!ring !lus the

,inetic energ' due to the &elocit' and mass o" the obIect attached

to the s!ring

E=1

2 k x

2+1

2m v

2

•6 am!litude o" oscillation G

!;H

• instant at end !oints8 KE is Aero and E is at ma6imum

• instant at equilibrium !osition E is Aero and KE is at ma6imum

G&elocit' is ma6imum

• there"ore8 total energ' in the s'stem=

Etotal=1

2k "

2=1

2 m vmax

2

•

ma6imum &elocit' o" an oscillator=

vmax=√ k

m "

Perio' an' "reuency of &=!

• !eriod o" oscillation=

23



T =2 pi√m

k

:. (he &imple Pen'ulum

• a perio' of a pen'ulums s$ing is inde!endent o" the mass o" theobIect hanging and &aries onl' b' the length o" the !endulum and

the gra&itational acceleration

• % length o" !endulum

• Amplitu'e J ma6imum dis!lacement "rom equilibrium !osition

24



;.0 8a5es

• Normall' /a&es tra&el as a disturbance in some medium

;.2 &=! an' 8a5es• +hen a /a&e !ro!agates8 each s!atial !oint on the /a&e mo&es in

S#

• 8a5elength *B %amba+ J horiAontal distance bet/een oscillations

;. "reuency 8a5elength an' &pee'

¿∆ x∨¿t =

#

T = f #

vwave=¿

;.7 (ypes of 8a5es

• (rans5erse $a5e J one in /hich the medium the /a&e is

oscillating through is mo&ing !er!endicular to the direction the

/a&e is !ro!agating

• %ongitu'inal $a5e J s!atial !oint in the medium the /a&e is

mo&ing through is oscillating in the direction the /a&e is

!ro!agating

;.10 8a5es an' /nergy

/nergy

• +a&e is a series o" S oscillations8 each o" these oscillations ha&e

the same am!litude and "requenc'

PE=1

2k "

2

• This is the case in general

•

Energ' transmitted b' a /a&e is !ro!ortional to the square root o"the am!litude o" that /a&e

Po$er an' Dntensity

• Po$er is a measure o" ho/ much energ' is transmitted !er unit

time G P=

W

t H

2*



• Dntensity J ho/ much !o/er !er unit area and is measured in /atts

!er square meter G+ m>2H

$ = P

"

• ; area /hich it is s!read

;.11 Complex 8a5eforms

!usical an' Vocal (one

• =armonics J are all signals /ith "requencies that are multi!les o"

the "requenc' o" the original sound

• armonics are due to 'istortion

E.0 &oun' an' =earing

E.2 &oun' 8a5es in !e'ia

• &oun' $a5e J generall' used to re"er to com!ression or strain

/a&es transmitted through a medium that ha&e sucient intensit'

and are a "requenc' that can be detected as sound

• Fltrasonic J "requenc' too high "or hearing GO20AH

• Dnfrasonic J "requenc' too lo/ "or hearing GP 20KAH

• &onic J range that human ear can hear G20A J 20,AH

Pressure 8a5es in 4ases

• &oun'$a5e J a mo&ing disturbance o" molecules o" the air

• Compressions J areas /here the molecules are closer together

• @arefactions J molecules are more s!arse

• &oun'$a5e is longitudinal

8a5es in &oli's an' %iui's

• Sound/a&es can be transmitted through solid or liquids b'

oscillation o" the molecules o" the medium• 9n solids8 /a&es can either be=

> ongitudinal Gcom!ressi&e and tensile strain /a&esH> Trans&erse Gshear strain /a&esH

8a5e &pee'

• S!eed o" sound is not ?6ed and it de!ends on the medium through

/hich is tra&els

• +hen tem!erature is higher8 so is the s!eed o" sound

2)



csound=√ %

&

• c s!eed o" sound

• bul, modulus• G densit' o" medium

• increases /ith sti<ness o" medium

• decreases /ith increasing densit'

E. Pitch an' %ou'ness

"reuency an' Pitch

• pitch J ho/ high or lo/8 determined b' /a&e "requenc'

• higher the "requenc'8 higher the !itch

• !itch J S9 unit A• consonance J t/o notes that sound !leasant together

• 'issonance J un!leasant combination o" notes

Amplitu'e an' Dntensity

• lou'ness largel' but not entirel' determined b' the am!litude o"

the !ressure uctuations

• amplitu'e related to intensit'

• intensity J a measure o" ho/ much energ' is trans!orted through a

unit area e&er' second G/atts(m2H

Dntensity %ou'ness an' the 'ecibel scale

• human ears can detect sound /a&es that &ar' b' 12 orders o"

magnitude

• decibel used to com!are sound intensit'

• sound intensit' le&el GQH

'=10log $

$ o

• 9o J 10>12+m>2

E. @esonance an' &oun' 4eneration

• (o generate soun' J something mo&es sucientl' to create an air

!ressure /a&e o" enough intensit'

(he =uman Vocal Cor's

• Vocal tract J ca&ities o" the mouth8 nasal ca&it' and !har'n6

2-



• $hanges in &ocal tract /ill alter resonant characteristics and alter

sound

• To create sound energ' source is needed

• ;ir "rom lungs used as energ' source

•

%arynx J &ocal cords8 t/o bonds o" muscular tissue

E.7 (he /ar

Anatomy

Huter /ar

• Pinna J sits outside the s,ull

• Au'itory canal and tympanic membrane Gear drumH

• Sound /a&es channelled and slightl' altered b' the !inna and canal

• These /a&es cause ear drum to &ibrate

!i''le /ar

• Hssicles J ligaments that sus!end a series o" small bones

• /ustachian tube J connects ossciles to oral ca&it'

• !alleus GhammerH J attached to t'm!anic membrane

• Dncus Gan5ilH J malleus connects to

• &taples GstirrupH J connected to incus and then connects to the

o&al /indo/

• H5al $in'o$ J through /hich mo&ement o" the ossicles causes

mo&ement in the uid inside the cochlea

Dnner /ar

• Cochlea J ca&it' encased /ith bone and ?lled /ith uid

• @oun' $in'o$ J in addition to o&al /indo/8 connects to cochlea

and mo&es in and out in res!onse to !ressure uctuations in the

cochlea

• $ochlea is internall' di&ided into t/o hal&es b' a membrane

• asilar membrane J sound /a&es are turned into signals

• S!eed o" !ressure /a&es in the uid>?lled cochlea are much greater

than that o" air

• ressure is basicall' the same all o&er at an' time

(he /ar an' the problem of impe'ance

%etting !ressure /a&es in the air to the bod's liquid interior=

• esonance in the ear canal and "ocusing b' the !inna hel!s

2



• Bssicles act li,e a set o" le&ers to slightl' am!li"' the &ibrations

• Di<erence in the siAe o" the ear drum and o&al /indo/ ha&e a

dramatic e<ect

• Force a!!lied to the ossicles is a !roduct o" the area o" the ear and

!ressure e6erted on it• Force is am!li?ed b' the bones and then a!!lied to a much smaller

o&al /indo/8 !roducing a larger "orce !er unit area8 hence larger

!ressure

• Ear reduces the transmission o" sound into the cochlea to reduce

the ris, o" damage

E.6 (he oppler /Iect

• Do!!ler e<ect J a!!arent !itch o" a sound is changed b' the relati&e

motion bet/een the sound source and the obser&er

• E<ect a!!lies "or electromagnetic /a&es as /ell as sound

2:



10.0 /lasticity &tress an' &train

10.2 (ension an' Compression

• &tress 3 is a measure o" the "orce !er unit area a!!lied to anobIect8 and the siAe o" the internal "orces acting on the obIect as a

reaction to the e6ternall' a!!lied "orces

• &train J measures the change in sha!e o" an obIect subIect to

stress

(ensile &tress an' &train

• (ensile stress 3 /hen an obIect is being subIected to stretching

"orces so that its length /ill increase

• ;chie&ed b' a!!l'ing "orces to o!!osite ends o" an obIect8 directed

a/a' "rom one another

• Stretches intermolecular bonds8 i" sucientl' high /ill brea, these

bonds

• (ensile stress J stretching "orce !er unit area

Tensile (tress=) = F

"

• F "orce a!!lied to each end

• ; cross>sectional area o" the obIect at right angles to the directiono" the stretching "orce

• 9ncreases length

• ;mount b' /hich obIect increases de!ends on=> The tensile stress a!!lied> The material it is made o" > The length o" the obIect

• Tensile strain J amount o" stretch !er unit length=

*= + ,

,0

• R amount b' /hich an obIect is stretched

• 0 original length o" the obIect

• 9n direction o" stretch

• =oo9e>s %a$ J amount o" stretch is !ro!ortional to the "orce

a!!lied

• Stress is !ro!ortional to strain

30



• Double the stress8 double the strain

• Joung>s !o'ulus *+ J !ro!ortionalit' constant8 ho/ much stress

is required to generate a gi&en strain in a material

• Strain is dimensionless8 units o" "orce !er unit area GNm>2 or aH

- =tensile stress

tensile strain=

F

"

+ ,

,0

• Stress 'oungs modulus 6 strain

• Joung>s !o'ulus J measure o" a materials resistance to

stretching8 does not de!end on siAe or sha!e o" obIect but onl' on

material

• Dsotropic J same oungs #odulus in all directions

• Anisotropic J di<erent oungs #odulus in all directions

Compressi5e &tress an' &train

• Compressi5e stress J tries to com!ress an obIect8 that is8 to

reduce its length

• Forces a!!lied on o!!osite ends directed to/ards one another

• De"ormation o" an obIect !ro!ortional to the amount b' /hich the

intermolecular bonds are shortened

•

Force !er unit area or com!ressi&e stress

$om!ressi&e "orce causes compressi5e strain

• oungs #odulus also de?ned "or a material under com!ression

- = compressive stress

compressive strain=

F

"

+ ,

,0

• For most materials8 oungs #odulus "or tension and com!ression

are the same• 5one e6ce!tion

• Cnder com!ression8 "orce is ta,en to be negati&e in &alue8 so R /ill

be negati&e8 so the stress and strain ha&e negati&e &alues

31



10.7 /lasticity

&tress-&train Cur5es

• atio o" stress to strain "or materials is constant o&er a certain

range and de!ends on t'!e o" material

• /lastic region J stress(strain relationshi! linear8 this range the

material /ill return to its original sha!e8 an' sha!e changes are

re&ersible

32



33



11.0 Pressure

11. Pressure

• Pressure is a measure o" the "orce e6erted !er unit area

P= F

"

• P !ressure

• " "orce a!!lied normal to the area

• A area

• ressure is a scalar quantit'

• Cnit !ascal G;H Nm2

&oli's• E6erts !ressure on /hate&er it rests on

• ressure de!ends on /eight and sur"ace area is acts on

• Solid stationar' on sur"ace8 do/n/ards !ressure /eight di&ided

b' sur"ace area o" contact

4ases

• %ases e6ert !ressure /hen the collide /ith sur"aces

• ressure de!ends on the a&erage magnitude o" these collision

"orces and on the number o" collisions !er second

• ;&erage "orce !er collision /ill de!end on ho/ "ast the molecules

are mo&ing on a&erage Gdetermined b' tem!H and the densit' and

s!eed /ill determine ho/ o"ten collisions occur

• ressure e6erted b' a gas is the same in all directions

%iui's

• igher densit' o" a liquid means additional !ressure at the bottom

o" a liquid sam!le due to the /eight o" liquid abo&e that !oint is

signi?cant

•

iquid e6erts a do/n/ards "orce as /ell as a side/ards "orce on thecontainer

11. ensity

• Fluid densit'=

&=m

.

34



• m mass

• 7 &olume

• De!ends on the solid or liquid com!osition but not on ho/ much

there is

•

&oli's(liui's J distinct densit'8 de!ends on a&erage length o"intermolecular bonds

• %ases J densit' de!ends on siAe o" container

11. Pascals Principle

• ascals rinci!le J !ressure a!!lied to an enclosed uid is

transmitted undiminished to e&er' !oint o" the uid as /ell as the

/alls o" the container

• ;s a consequence8 in a static liquid the !ressure at de!th h8

de!ends on the !ressure a!!lied to the sur"ace and ho/ much liquid

there is abo&e that !oint e6erting additional !ressure

Ph= P surface+ &gh

∆ P= &g ∆ h

• !ressure is greater at a lo/er !oint

• basis o" h'draulic s'stems J i" a !ressure is a!!lied to the sur"ace o"

a static liquid8 the !ressure increases b' the same amount at all

other !oints G!ascals !rinci!leH• /or, done "orce 6 distance

• the !ressure at a !oint in a liquid is the same in all directions Gsame

"orce !er unit areaH

• "orce is al/a's e6erted !er!endicular to the area

• in order "or a liquid to be in equilibrium8 the !ressure must be the

same in all directions

3*



12.0 uoyancy

12.2 (he uoyant "orce

Archime'e>s Principle

• buo'ant "orce J is equal to the /eight o" the uid that the obIect

dis!laces

• buo'anc' J is the u!/ard "orce e6erted on an obIect that is "ull' or

!artiall'8 submerged in a uid resulting "rom the increase in

!ressure /ith de!th.

F /uoant =mf g= & f . f g

F net =mg− &f . f g= &o/0 . o/0 g− & f . f g

• i" obIect is "ull' submerged8 the /eight "orce is equal to the buo'ant

"orce !lus the normal "orce

• i" the obIect is stationar' in the /ater the net "orce is Aero

3)



1.0 "lui' ynamics of #on-Viscous "lui's

1.2 eLnition of Key (erms

• incompressible Mui' J the uid has a constant densit' throughout• 5iscosity J the resistance o" a uid to o/

• laminar Mo$ J a situation in /hich la'ers o" uid slide smoothl'

!ast each other. $haracteristic o" lo/er uid &elocit'

• turbulent Mo$ J non laminar o/8 irregular and com!le6 /ith

mi6ing and eddies. Bccurs at higher &elocities or /here there are

obIects in the o/ !roducing large changes in &elocit'

• &treamlines J "amil' o" cur&ed lines that are tangential to the

&elocit' &ector o" the o/ Gal/a's in the same direction o" o/H.

ro&ide a sna!shot o" o/ throughout the uid a' an instant o" time

1. (he euation of Continuity

Volume "lo$ @ate

• Volume Mo$ rate Gf H ho/ much uid is mo&ing across some

sur"ace Gm3(sH

• For an incom!ressible uid=

f =∆ .

∆ t =

" ∆ x

∆ t = "v

Continuity of "lo$

• +hen no uid is gained or lost8 &olume o/ rate is constant along

!i!e or channel

• Conser5ation of mass J amount o" material entering one end o"

the !i!e must be the same as the amount coming out the other end

• ;lso same amount !er unit time

• Fi6ed mass ?6ed &olume8 there"ore constant &olume o/ rate

• $ontinuit' equation=

"1 v1= "2 v2

• #ulti!le !i!es o/ing8 sum equals sum o" !i!es o/ing out

• +hen liquid enters more com!ressed Aone8 &elocit' increases

3-



1. ernoulli>s /uation

ernoulli>s Principle an' Dncompressible "lui' "lo$

• +hen &iscosit' is neglected8 increase in uid &elocit' is

accom!anied b' a decrease in !ressure and(or decrease in

gra&itational !otential energ'

• 7alid "or most liquid or gases /hen no e6!ansion o" com!ression is

ha!!ening

• 9" uid o/ is laminar and /e can ignore the e<ects o" "riction

• 5ernoullis equation=

P+1

2 & v

2+ &gh=constant

• h J height o" the !oint abo&e selected re"erence height• constant sum is constant along a streamline

/nergy ensity

• pressure "orce !er unit area

• 1 a 1 Lm>3

• ressure can be thought o" as energ' !er unit &olume

• Kinetic energy !er unit &olume 1

2 & v

2

• 4ra5itational potential energy !er unit &olume &gh

Pressure an' Velocity

• T/o !oints on a streamline=

P1+1

2 & v1

2+ &gh1= P2+

1

2 & v2

2+ &g h2

• No change in height8 E remains the same=

1

2 & v2

2−

1

2 & v1

2= P1− P2

• $hange in !ressure gi&es change in ,inetic energ' !er unit &olume

Gi" &elocit' at 2 higher8 !ressure at 2 is lo/erH

• ressure lo/er at more constricted region /here &elocit' is higher

3



Applications of ernoulli>s /uation

Fluid Flow out of Tank

• Torricellis Theorem J the s!eed o" eu6 Gouto/H through an outlet

!i!e is !ro!ortional to the square root o" the head heightv=

√ 2 gh

s−¿ho

h¿

2 g¿vo=√ ¿

Plaque Deposits and Aneurysms

• laque de!osits narro/ed blood &essels

• ;neur'sm /idened blood &essels

• Stenosis J case o" narro/ing

> 5lood &elocit' must be increased> There"ore decrease in !ressure> #a' result in "urther narro/ing> +hen arter' is narro/ed8 o/ /ill become more turbulent

G!ossibl' damaging arter' /allH

• ;neur'sm J localised8 balloon>li,e bulge in an arter'> adius increases8 &elocit' decreases> ressure increases

3:



17.0 "lui' ynamics of Viscous "lui's

17.2 Viscosity

• +hen a shear stress is a!!lied to a uid8 it cause it to o/8 that is8to de"orm continuousl'

• Shear stress F

"

• Viscosity J the resistance o" a uid to o/

• De?ned b' ?nding the shear stress required to generate a shear>

strain rate o" one !er second

• Strain is dimensionless8 it is a ratio o" distances

• @ate of change of strain=

∆ x / ,∆ t

=v

,

• uid de!th

• & constant s!eed

• some uids J shear strain is !ro!ortional to the shear strain rate8

and the !ro!ortionalit' constant is the uid &iscosit'

F

" =1

v

,

• &iscosit' !ro!ert' o" a uid

• units o" &iscosit'= Nsm>2 a s

Poiseuilles %a$

• o/ o" &iscous uid along a !i!e8 requires a !ressure di<erence to

o&ercome the &iscosit'

• the narro/er the !i!e8 the larger the required !ressure di<erence

• the longer the !i!e8 the larger the required !ressure di<erence• higher &iscosit' higher !ressure di<erence

• oiseuilles a/ J &olume "lo/ rate "or a "luid o" &iscosit'8 U8 through

a c'lindrical !i!e o" length8 l8 and radius8 r8 /hen the !ressure

di<erence bet/een the ends is R is=

Ϝ = + P2 r

4

8 1l

40



Key Concepts

• Viscous Mui' 3 a &iscous uid is one in /hich /e cannot ignore the

e<ects o" "riction /ithin the uid and bet/een the uid and

neighbouring inter"aces

•

Viscosity *N+ 3 ; measure o" the internal "riction o" a uid. 9t is a!ro!ert' o" a !articular uid and is a measure o" the uids

resistance to o/. The &iscosit' has units N s m>28 /hich are the

same as a s.

41



1:.0 (emperature an' the Oeroth %a$

1:.2 (hermal /uilibrium

• (emperature J measure o" ho/ hot or cold something is• (hermal euilibrium J /hen s'stems are in thermal contact8 the'

e6change energ' until an equilibrium state is reached and no more

net energ' trans"er occurs

• Oeroth %a$s of (hermo'ynamics J i" t/o s'stems8 ; and 58 are

in thermal equilibrium8 and a third s'stem8 $8 is in thermal

equilibrium /ith ;8 the it is also in thermal equilibrium /ith 5.

• (hermal energy J ,inetic energ' associated /ith the random

motion o" atoms /ithin molecules eg. otational and &ibrational

•

Thermal energ' de!ends on the number o" molecules in an obIectand molecula' com!osition8 as /ell as tem!erature

• +hen t/o obIects o" di<erent tem!erature are !laced in contact8 the

collisions occur bet/een the molecules in the t/o obIects

• Thermal energ' is trans"erred "orm the hotter obIect to the colder

obIect through these collisions

• Thermal energ' that is trans"erred is ,no/n as heat

• The mo&ement o" thermal energ' due to a tem!erature di<erence is

,no/n as heat transfer

• Thermal equilibrium is a d'namic equilibrium as collisions bet/een

molecules continue to trans"er thermal energ'

• ;t thermal equilibrium8 equal amounts o" energ' are being

trans"erred in each direction

42



1E.0 Phase an' (emperature Change

1E.2 Phase Change

• &oli' J de?nite sha!e and &olume8 not "ree to mo&e onl' &ibrate• %iui' J ?6ed &olume Gat !articular !ressure and tem!H but sha!e

de!endent on container8 molecules are "urther a!art than solid state

• 4as J molecules are "ar a!art on a&erage8 sha!e and &olume ?6ed

b' container

• Vaporisation J liquid to gas

• Con'ensation J gas to liquid

• !elting J solid to liquid

• "ree?ing J liquid to solid

•

&ublimation J solid to gas• eposition J gas to solid

Phase iagrams

• oiling point J o" a liquid is the tem!erature at /hich the liquid

and &a!our !hases are in equilibrium8 de!ends on !ressure> 9" the &a!our !ressure o" the gas !hase is lo/er than the

saturation &a!our !ressure8 then molecules can continue to

brea, a/a' "rom the liquid and Ioin the gas !hase

• Vapour pressure J the &a!our !ressure o" a substance is the gas

!ressure created b' the solid or liquid !hase8 and is a consequenceo" the "aster molecules brea,ing a/a' "rom the liquid or solid

• (hermo'ynamic euilibrium J rate at /hich the molecules lea&e

the liquid and the rate at /hich the' re>Ioin it are the same

• &aturation 5apour pressure > de!ends onl' on tem!erature

• critical temperature > &a!our densit' and liquid densit' are equal

at this tem!erature Ghigh tem!H

• abo&e critical tem! is called a super critical Mui' as the liquid

!hase does not e6ist and there is no distinction or !hase boundar'

bet/een liquid and gas• triple point > solid8 liquid and gas !hases are all in thermod'namic

equilibrium

• tri!le !oint occurs at a unique tem! not a<ected b' &olume o"

number o" molecules

• belo/ tri!le !oint8 solid8 liquid and gas cannot co>e6ist in

equilibrium8 instead &a!our co>e6ists /ith the solid !hase8 !ro&ided

&olume is large enough

43



• com!ressing a gas "a&ours condensation as the rate o" collisions

bet/een molecules are increases

• bo'leVs la/ G7H brea,s do/n at lo/ tem!eratures /hen attraction

bet/een molecules becomes signi?cant and the gas begins to

condensate into a liquid

Phase Changes an' %atent =eat

• to change the !hase o" a substance requires thermal energ'

• soli' to liui' > bonds bet/een molecules bro,en /ith addition o"

energ'

• liui' to gas > energ' required

• gas to liui' or liui' to soli' > thermal energ' must be remo&ed

• amount o" energ' required to change the !hase o" a substance

de!ends on the substance and the amount o" the substance=

Q = mL

• Q amount o" heat require "or !hase change

• m Q mass o" substance

• % Q latent heat o" !hase change

• latent means hidden

• /hen a substance e6ists in both !hases simultaneousl'8 the

tem!erature does not change

•

di<ers "or each t'!e o" !hase change and has some de!endenceon tem!erature

• %f heat o" "usion8 energ' required to change 1,g o" the substance

"rom solid to liquid

• %5 heat o" &a!ourisation8 energ' required to change 1,g o" the

substance "rom liquid to &a!our

• %s heat o" sublimation8 heat required "or substances that go

straight "rom solid to &a!our !hase

• !ositi&e8 energ' added8 s'stem gains thermal energ'

• negati&e8 energ' ta,en out8 s'stem looses thermal energ'

• latent heat o" !hase change is de!endent on tem!

1E. (emperature Changes

=eat an' (emperature

• /hen a substance has thermal energ' trans"erred to it8 it can

!roduce a !hase change

• other !ossible result is a change in tem!

44



• amount o" tem! change de!ends on substance being heated

• heat is energ' trans"erred due to a tem!erature di<erence

• heat joules

• an obIects internal energ'8 hence tem!8 can be increased b' doing

/or, on it

&peciLc =eat

• tem!erature is the measure o" the a&erage ,inetic GthermalH energ'

o" the molecules in a substance

Q =mc∆ T

• R( tem! increase caused b' W

• c Q s!eci?c heat ca!acit'8 the amount o" heat required to increase

the tem!erature o" 1,g o" a !articular substance b' 1K • speciLc heat capacity > de!ends on substance8 tem!erature and

!hase o" substance

• 1 calorie GcH 4.1)L

• ,cal $al G$H

1E. /nergy Conser5ation

• obIects in thermal contact e6change heat until thermal equilibrium

is reached

• at this !oint net e6change o" energ' ceases and obIects ha&e the

same tem!

(he &imple Case - #o Phase Change

• /hen the amount o" energ' trans"erred does not cause a change o"

!hase

• t/o obIects in thermal contact isolated "rom their surroundings

Qobj 1=Qobj 2

• sum o" heat out!uts equals Aero

(hermal /uilibrium $ith Phase Change

• !re&ious equation still &alid8 ho/e&er8 no/ need to include the heat

trans"er that occurs during the changes in !hase

• eg. /ater and ice=

mwater cwater ( Tf - Ti water !+mice cwater ( T f - Ti ice !"m ice Lf water

4*



4)



21.0 =eat (ransfer

=eat (ransfer by Con'uction

• heat con'uction > the trans"er o" thermal energ' "rom an obIect athigher tem!erature to an obIect at lo/er tem!erature

• these t/o obIects can be connected b' a medium and thermal

energ' is trans"erred &ia &ibration motion "rom one molecule to

another or &ia conduction electrons /ondering "rom atom to atom

• rate o" heat trans"er through material /ill de!end on its microsco!ic

structure

• thermal con'ucti5ity G9 H > !ro!ert' o" a material /hich tells us

ho/ readil' heat is trans"erred through it

•

thic,ness and cross>sectional area o" an obIect /ill e<ect rate o"energ' trans"er

• more cross>sectional area8 more molecules in contact

• more thic,ness8 more molecules to !ass energ' through

• a bigger tem!erature di<erence8 a higher trans"er rate

∆ Q

∆t =

#$T

% =&con%'ction $ ∆T

•

∆ Q

∆T rate o" heat trans"er b' conduction

• 9 thermal conducti&it'

• ' thic,ness

• A cross sectional area o" medium(material in contact

• R( tem!erature di<erence bet/een sur"aces se!erated b'

thic,ness d

• coecient o" conduction heat trans"er #

%

•

hcon'uction + m

>2

,

>1

• 9 + m>1 ,>1

Coe<cient of =eat (ransfer

• tells us ho/ ra!idl' heat is being trans"erred !er square meter o"

sur"ace area8 /hen there is a 1K tem!erature di<erence

4-



Con'uction (hrough !ultiple %ayers

• to get h>&alues "or multi!le la'ers /e add the reci!rocal h>&alues

together

21. Con5ection

• heat trans"er b' uid con&ection occurs as a result o" the bul,

motion o" a uid

∆ Q

∆t =&convection $ ∆ T

21. @a'iation

• all obIects radiate energ' in the "orm o" electromagnetic radiation

• rate and "requenc' range determined b' tem!erature

(he &tefan-olt?mann %a$

• gi&es the rate at /hich an obIect radiates electromagnetic /a&es

∆ Q

∆ t ¿emitte%=*)" T

4

• S sur"ace emissi&it'

• T Ste"an 5oltAmann $onstant *.)- 6 10> +m>2K >4

• A sur"ace area

• ( absolute tem!erature

• X is bet/een Aero and one

∆ Q

∆ t ¿net=

∆ Q

∆ t ¿s'rface−

∆ Q

∆ t ¿environment

∆ Q

∆ t ¿net=&ra%iation$ ∆ T

• hradiation> 4XYT3 radiati&e sur"ace heat trans"er coecient

• ho/ /ell a sur"ace emits radiation is determined b' ho/ /ell it

absorbs it

• dull blac, sur"aces ha&e highest emissi&ities G0.:>1H

• blac9bo'y > theoretical !er"ect emitter(absorber has emissi&it' o" 1

4



• at tem!erature o" human bod'8 obIects emitt no &isible light8 onl'

in"rared

Colour an' (emperature

• /a&elength8 hence colour o" light emitted b' a hot obIect is tem!

de!endent

• 8ien isplacement %a$ > /a&elength at /hich most emission

occurs GZma6H is related to tem!

# max ¿ /

T

• ( absolute tem!erature

• b is a constant8 2.: 6 10>3mK

21.7 Combine' (ransfer Process

• conduction8 con&ection and radiation all contribute to the heat

trans"er "rom an obIect

• hsur"ace hcon&ection hradiation

• consider equilibrium state > tem! o" sur"aces and la'ers constant8

heat lea&es an' la'er at the same rate it enters la'er

• heat trans"er &ia conduction through !ersons tissue=> equal to rate o" heat trans"er &ia conduction through their clothing

> /hich is equal to

∆ Q

∆ t &ia conduction radiation "rom clothing

sur"ace to surroundings

∆ Q

∆ t htissue ;GTcore > TS,inH

hclothing ;GTs,in > Touter sur"ace o" clothingH

hsur"ace ;GTouter sur"ace o" clothing > TsurroundingsH

htotal ;GTcore > TsurroundingsH

4:



22.0 (hermo'ynamics an' the o'y

22.2 (he "irst %a$

• energ' is conser&ed= energ' can be trans"erred "rom one "orm toanother8 but it can be neither destro'ed nor created

• total energy of a system *F+ > measure o" the amount o" energ'

in the s'stem is the ,inetic energ' o" the molecules and the &arious

"orms o" !otential energ'

∆ ( = Q - )

• RF change in total internal energ' o" a s'stem

•

net heat trans"erred to the s'stem• 8 net /or, done b' the s'stem

22. /nergy an' the o'y

• metabolism > energ' obtained "rom "ood through the biochemical

reactions /hich the !otential energ' o" "ood molecules is con&erted

to other "orms

three $ays the bo'y can gain or lose energy *RF+1. eat trans"er /ith surroundings GWH2. 5od' doing /or, on surroundings G+H

3. %ain o" material b' the s'stem GEH∆ = Q-)"*

• / energ' gained as the result o" metabolism o" "ood

!etabolism =ypothermia an' =yperthermia

• hypothermia > metabolic rate lo/er than our o/n rate o" heat loss

to en&ironment8 /e /ill lose heat energ' and core tem! /ill

decrease. Sta' in this situation too long results in h'!othermia

belo/ 3- deg $

•

hyperthermia > metabolic rate e6ceeds rate o" heat loss8 core tem!/ill increase Gheat stro,eH

• net rate of energy lost rate o" heat loss > rate o" metabolism

• total energy lost net rate o" energ' loss 6 time

/<ciency

• n de?ned as ratio o" mechanical /or, done b' the bod' to the

energ' used "or mechanical /or,

• 8 /or, done b' the bod'

*0



• / > RF decrease in internal stored energ'

• equi&alent to /or, out!ut "rom the bod' !lus the heat lost G+>WH

n=)

*-∆ =

)

)-Q

• bod' uses resources to do /or, RF U 0

• bod' more inta,e then required "or /or,8 stored "at8 RF 0

• bod' neither uses stored energ' reser&es or adds to stored reser&es

RF Q 0

• RF 08 s'stem gains internal energ'

• 08 s'stem gains heat

• 80 8 /or, done b' the s'stem

• E is al/a's P0

• Second a/ Thermod'namics > heat o/s s!ontaneousl' "rom asubstance at higher tem!erature to a substance at lo/er

tem!erature8 not the other /a' round

• Third a/ Thermod'namics > it is not !ossible to lo/er the

tem!erature o" an' s'stem to absolute Aero in ?nite number o"

ste!s

*1



2.0 &tatic /lectricity

2.2 Charge

• /lectric charge J attracti&e "orce bet/een electrons and !rotonsdue to intrinsic !ro!ert' called electric charge

• /lectrostatic force or electric Lel' J "orce due to electric charge

• Electric charge comes in t/o di<erent t'!es= negati&e and !ositi&e

• The' carr' the same magnitude o" charge

• #eutral J !article that does not ha&e an electric charge

• Don J has a net charge

• i,e charges are re!ulsi&e

• Force bet/een unli,e charges J attracti&e

> Force decreases in strength as se!aration o" charges increase

• S9 Cnit o" $harge J $oulomb G$H

• Coulomb J quantit' o" charge !assed in one second through cross>

section o" an electrical conductor carr'ing one am!ere o" current

• Current J ho/ much charge is mo&ing through a ?6ed area !er

second

• Charge conser5ation J net charge o" an isolated s'stem ne&er

changes8 as !articles are created or destro'ed8 other !articles are

created or destro'ed to ,ee! the o&erall charge o" the s'stem

constant.

• uantisation of charge J net charge o" an' s'stem is an integermulti!le o" the smallest amount o" charge that can be measured on

an' "ree !article

• Smallest amount o" charge is the magnitude o" the charge on an

electron or !roton8 e8 elementar' charge

• $harge on an electron >1.)02610>1:$

2. Con'uctors an' Dnsulators

• Con'uctor 3 material /hich charge o/s through easil'

•

Dnsulator 3 charge does not o/ through "reel'• #etals generall' good conductors

• $ommon insulators J glass8 rubber8 !lastic

Key Concepts

• Charge * or + 3 Electric charge is a "undamental !ro!ert' o"

matter8 and comes in t/o t'!es8 ,no/n as !ositi&e or negati&e8

/hich are re"erred to as the sign o" the charge. The S9 unit o" charge

is the coulomb Gs'mbol $H

*2



• /lementary charge *e+ 3 The smallest Gnon>AeroH charge

magnitude that can be carried b' an' obser&able elementar'

!article. Electrons ha&e a charge o" Je and !rotons ha&e a charge o"

e. 9t has the &alue o" 1.)02610>1: $.

•

/lectron 3 ; "undamental subatomic !article that carries a negati&echarge o" e>1.)02610>1: $8 and has a mass :.10:610>31 ,g.

• Atom 3 usuall' de?ned as the smallest entit' that retains the

chemical !ro!erties o" an element. ;n atom consists o" a nucleus

and electrons8 /ith the number o" electrons equalling the number o"

!rotons in the nucleus.

• Don 3 an atom that has gained or lost electrons and consequentl'

carries a net !ositi&e or negati&e charge

• Con'uctor 3 a material that /ill readil' !ermit the o/ o" electric

charges

• Dnsulator 3 a material that does not readil' !ermit the o/ i"

electric charges

• Polarisation 3 in electrostatics8 the !artial or com!lete se!aration

o" !ositi&e and negati&e electric charge in a s'stem

*3



2. 0 /lectric "orce "iel' an' /lectric "iel'

2.1 Dntro'uction

• $harges inuence each other at a distance• $harges create a ?eld8 creates a "orce on other charges !laced in

the ?eld

2.2 Coulomb>s %a$

• Force e6ists bet/een charged !articles

• #agnitude o" the "orce de!ends on the magnitude o" each charge

and ho/ "ar a!art the' are

• Coulomb>s %a$

| F 1

on 2|=| F 2

on 1|=k |3

13

2|r

2

• q magnitude o" charges

• r distance se!arating charges

• , e6!erimentall' determined constant o" !ro!ortionalit'

•k =

1

4 2 *o

=+ x 10+ N m

24

−2

• *o !ermitti&it' i" "ree s!ace

• Direction o" the "orce is along the line Ioining t/o charges

• Force attraction i" charges are o!!osite signs and re!ulsi&e i" the'

are the same

2. &uperposition of /lectric "orces

• Principle of &uperposition J the net "orce on an obIect that is

interacting /ith more than one other obIect is the &ector sum o" the

"orces "rom all the interactions

F on 1net = F 2 on1+ F , on1+ F 4 on 15

2. Dn5erse &uare %a$

h'sical quantities that obe' the in&erse square la/=

• Electric ?eld strength "rom a !oint source "alls /ith distance squared

*4



• 9ntensit' o" electromagnetic radiation "rom

a !oint source "alls /ith distance squared

• %ra&itational attraction to a mass "alls /ith

distance squared

2.7 (he /lectric "iel'

• The electric Lel' is a /a' o" describing

ho/ a con?guration o" charges a<ects the

surrounding s!ace

• De?ned in terms o" magnitude and direction

o" the electric "orce !er unit o" charge that a

charged obIect /ould be subIected to at a

gi&en !oint in s!ace

• S9 unit= N $>1

• o/ much "orce a 1$ /ould e6!erience• Force on a charge is a &ector quantit'

• Electric ?eld is also a &ector quantit'8 /ith its direction being that in

/hich a !ositi&e charge /ould e6!erience a "orce=

E=%

3

(est charge J is a nominal Gand !ossibl' imaginar'H charge !laced

at some !oint in s!ace that is small enough not to cause an'signi?cant change in the s'stem o" charges /hich are being

in&estigated8 but /hich allo/s us to in&estigate the electric ?eld at a

!oint in s!ace

/lectric Lel' 'ue to a point charge> W !oint charge creating the ?eld> q test charge !laced at a distance r "rom the ?rst charge> The magnitude o" the "orce on the test charge=

F =k 63

r2

• #agnitude o" electric ?eld=

E= F

3

• ;nd "or a !oint charge W /e there"ore ha&e=

**



E=k 6

r2

• The direction o" the ?eld is the same as the direction that the "orce

/ould be on a !ositi&e charge J radiall' out/ard "rom the sourcecharge i" !ositi&e8 to/ards the source charge i" it is negati&e

2.6 /lectric "iel'

iagrams

• Vector Lel'

*)



• "iel' %ines

• e!resents the direction o" the $oulomb "orce

• Not &ectors8 ha&e no length

• Strength o" the ?eld is indicated b' ho/ close together the lines are[

the closer together the ?eld lines are8 the stronger the ?eld is

• Dra/n starting at !ositi&e charges

and ending at negati&e charges

• Electric ?eld line dra/n starting and

ending in "ree s!ace onl' i" the

source charges are outside theregion being de!icted

• Electric ?eld lines cannot cross

• Fniform electric Lel'

• arallel !lates carr'ing a uni"orm

charge distribution8 /ith !ositi&e

charge on one !late and negati&e on

the other

• Nearl' the same magnitude and

direction e&er'/here bet/een the!lates G!ro&ided distance bet/een

the !lates is small in com!arison

/ith the !late areaH

• /lectric 'ipole Lel'

*-



• Equal magnitude !ositi&e and negati&e

charges se!arated b' some distance

• Field lines !oint "rom !ositi&e to

negati&e

*



2.: &uperposition of /lectric "iel's

• The net electric ?eld at an' !oint in s!ace can be "ound b' the

&ector sum o" the ?elds at that !oint due to all the charges !resent

• ;t each !oint in s!ace8 the resultant electric ?eld &ector is the sum

o" the electric ?eld &ector that /ould be created b' the lone !ositi&e

charge and that /e /ould get "rom Iust the negati&e charge

Key Concepts

•

Coulomb>s %a$ J the la/ that describes the "orce bet/een t/ocharges. The "orce is !ro!ortional to the !roduct o" the magnitudes

o" the charges and in&ersel' !ro!ortional to the square o" the

distance bet/een them

• "iel' J a numerical quantit' associated /ith each !oint in s!ace. ;

?eld can be scalar Gas in the case o" a tem!erature ?eldH or &ector

Gli,e &elocit' or electricit' ?eldH

• /lectric "iel' */+ J The &ector ?eld !roduced b' electric charge.

The electric ?eld &ector is de?ned as the $oulomb "orce !er unit

charge that a \test charge /ould e6!erience i" !laced at that !oint

in s!ace8 and its magnitude is the same as the magnitude o" the

$oulomb "orce that /ould be e6erted on a 1 $ \test charge. The

direction o" the electric ?eld &ector is in the same direction as the

$oulomb "orce on a !ositi&e \test charge. The electric ?eld is

measured in units o" N$>1 Gor equi&alentl' in &olts>!er>meter8 7m>1H.

*:



27.0 /lectrical Potential an' /nergy

27.2 /lectrical Potential /nergy

• e!resented b' the s'mbol C• estricted to sim!le case /here

"orce is not changing Gin this boo,H

27. /lectrical Potential

• The electrical !otential at a !oint in

s!ace does not de!end on the

charge o" an' obIect !laced at that

!oint8 but is a measure o" the

electrical !otential energ' that acharge /ould ha&e i" it /ere !laced

at that !oint

• Similar to electric ?eld conce!t J

"orce on a charge i" it /ere !laced at

a !articular !oint in s!ace

• The electrical !otential has a &alue

at each !oint in s!ace /hether or

not it is occu!ied

• The !otential is a !ro!ert' associated /ith a !oint in s!ace caused

b' the !resence o" an electric ?eld

• The electrical !otential is a scalar ?eld J it has a &alue at each !lace

but it is directionless

• Electrical !otential=

. =7

6

• C is the electrical !otential energ' o" charge W

• S9 unit o" electrical !otential= 7olts G7H[ 171L$>1

• Electrical !otential is inde!endent o" the charge G]test charge^ not

the source charges creating the ?eldH

• T/o di<erent charges !laced in the same !osition /ould ha&e

di<erent !otential energies8 but the' /ould ha&e identical !otentials

)0



2. /lectrical Potential an' 8or9

• +hen a charge mo&es due to the inuence o" an electric ?eld8 /or,

is done on the charge b' the electric ?eld.

• The /or, done on the charge is equal to the reduction in electrical

!otential energ'

+ 6=−W elec

• Eg. 9" a charge mo&es to

a !osition /here its

electrical !otential

energ' is lo/er8 the

change in electrical

!otential is negati&e8and the charge has

!ositi&e /or, done on it

b' the ?eld

• The abo&e does not

consider the "orces

in&ol&ed8 onl' /or, done

b' electric ?eld

W elect = F + x

• R6 distance the charge is mo&ed in the direction o" the "orce

• F "orce electric ?eld e6erts on the charge G F =3E¿

W elect =3 E + x

• +e can no/ deri&e an equation "or the change in electrical !otential

energ' o" a charge as it mo&es "rom one !osition to another=

+ 7 =−3E + x

• otential di<erence bet/een t/o !oints is G7C(qH

+ . =− E + x

• Cnits N$>1 or 7m>1

)1



2.: (he =eart an' /C=

• Electrocardiogram GE$%H

• +hen a heart is beating normall' an electrical signal is generated

and tra&els through the heart muscle

•

Electrical signal causes contraction o" the heart muscles and isultimatel' res!onsible "or the s'nchronised beating o" the heart

• ; t'!ical heart muscle cell has a !otential di<erence o" around

:0m7 and this e6ists bet/een the inside and outside o" the cell

membrane8 /ith the outside o" the cell being !ositi&e. This is called

the ]resting !otential^ and a cell /ith this !otential di<erence is

called ]!olarised^.

• +hen the trans!ort o" ions "rom one side o" the membrane to their

other changes the sign o" this !otential di<erence8 the cell becomes

]de!olarised^ and contracts

• 5e"ore the /a&e o" electrical acti&it' that

causes contraction !asses through8 the cells

are all !olarised. ; ner&e cell sends a signal

to these cells to cause them to become

!ermeable to the charges that are sitting on

the sur"ace.

• The net result is that the charge distribution

loo,s li,e a line o" se!arated !ositi&e and

negati&e charges that s/ee! do/n the heart

• This tra&elling electrical signal can be modelled as an electric di!oleGa se!aration o" !ositi&e and negati&e chargeH that changes strength

and siAe /ith time. This di!ole creates an electrical !otential

throughout the bod' ca&it'.

• Electrodes !laced on the s,in can measure this electrical !otential

GE$%H

Key Concepts

• /lectrical Potential *V+ J the !otential energ' !er unit charge at

each !oint in s!ace. The electrical !otential is a scalar ?eld. The S9unit o" electrical !otential is the 7olt8 s'mbol 7. Bne 7olt is

equi&alent to one Loule !er $oulomb

• /lectrical Potential iIerence *RV+ J The di<erence in electrical

!otential bet/een t/o !oints. otential di<erence is measured in

7olts G7H. The electrical !otential is o"ten Iust re"erred to as the

\&oltage.

)2



• /lectrical Potential /nergy *F+ J The !otential energ' stored in a

s'stem o" charges. The electrical !otential energ' ma' be thought

o" as the energ' required to bring the charges to !ositions the'

occu!'. The electrical !otential energ' is also the ma6imum amount

o" /or, that a s'stem o" charges ma' do i" unconstrained. 9t isusuall' gi&en the s'mbol C and is measured in Loules.

)3



26.0 Capacitance

26.1 Dntro'uction

• icture charged !lates carr'ing the same magnitude charge but /ith

o!!osite signs se!arated b' some distance

• Energ' stored in this con?guration _ and electric ?eld e6its as /ell

as a !otential di<erence bet/een the !lates

• $a!acitance is a measure o" the ca!acit' o" the circuit element to

store charge

• $ircuit elements ma' be designed s!eci?call' to store charge >

ca!acitors

26.2 (he Capacitor

• $a!acitor J a de&ice /hich stores electric !otential energ' in some

"orm o" a se!aration o" some charge

• The region bet/een the !lates has an electric ?eld !resent and a

!otential di<erence

E= $

*o

6

"

• E electric ?eld strength

• ; area o" each !late

• W magnitude o" the charge o" each !late

•*o constant8 !ermitti&it' o" "ree s!ace G.*4610>12Fm>1H

• Field bet/een the t/o charged !arallel !lates is uni"orm

• otential di<erence bet/een t/o !lates=

. = Ed

• d distance bet/een !lates

• 7 R7

6

. =*o

"

d

• For a !articular arrangement o" !lates8 ; and d do not change

)4



• $a!acitance=

4 =|6|

|. |

• S9 unit Farad GFH

• arallel !late ca!acitor=

4 =* "

d =*r *o

"

d

•*o &acuum

• elati&e !ermitti&it'=

ϵ r= *

*o

• egardless o" the ca!acitor sha!e8 $ al/a's W(7

26. /nergy &tore' in a Capacitor

• To change the ca!acitor8 /or, needs to be done to se!arate the

charges

• +or, done mo&ing a charge W o&er a !otential di<erence 7 is=

|w|=| + 7 |=|.6|

• Energ' stored in a ca!acitor is the same as the /or, done in

charging it

• C J energ' stored in a ca!acitor=

7 =1

2

62

4 =

1

26. =

1

26.

2

Key Concepts

• Capacitor 3 a de&ice /hich stores energ' b' se!arating charge.

Bne ,ind is the !arallel !late ca!acitor /hich stores charge W and

JW on t/o metal !arallel !lates se!arated b' air or a dielectric

material

)*



• Capacitance *C+ 3 ; measure o" the amount o" charge on each

!late o" a ca!acitor "or a gi&en electrical !otential across that

de&ice. The S9 unit o" ca!acitance is the "arad8 s'mbol F.

• ielectric 3 an insulating material used in a ca!acitor8 usuall' one

/hich does not brea, do/n at high &oltages. The dielectric materialbecomes !olarised8 causing the ca!acitor to ha&e a large charge

accumulation "or a gi&en !otential di<erence

• Permitti5ity 3 a quantit' that describes ho/ a material changes an

electric ?eld. The higher the !ermitti&it' o" the material8 the more

the electric ?eld /ithin it is reduced. The !ermitti&it' i" usuall' gi&en

the s'mbol X. The relati&e !ermitti&it'8 Xr8 gi&es the !ermitti&it' as a

"raction o" the !ermitti&it' o" "ree s!ace8 Xo ` .*4610>12Fm>1.

• ielectric constant 3 another term "or the relati&e !ermitti&it'

))



2:.0 irect Currents an' C Circuits

2:.1 Dntro'uction

• Electrical "orces ma' be used to trans"er energ' and in"ormationbet/een t/o !oints

2:.2 /lectric Current

• /lectric current 3 o/ o" charges G9H

• Electric current is a measure o" the rate at /hich charge mo&es

across a gi&en cross>sectional area

$ = + 6

+ t

• RW net charge crossing the area in time Rt

• S9 unit o" current am!ere ;8 one $oulomb o" charge !er second

• 1 ampere J stead' current that8 /hen o/ing in straight !arallel

/ires o" in?nite length and negligible cross>section8 se!arated b'

distance o" 1m in "ree s!ace8 !roduces a "orce bet/een the /ires o"

2610>-N !er m length

• Direction o" current is direction that !ositi&e charges /ould o/

• Direction o" so called \con&entional current is o!!osite to the /a'

the electrons are mo&ing

2:. Current "lo$ an' rift Velocity

• ensity J number o" electrons !er unit &olume

• 7 &olume o" segment /ith length8 l8 and cross>sectional area8 ;.

G7;lH

• Total amount o" mobile charge in segment=

+ 6=3 n.

• n densit' o" conduction electrons Gthere are n7 electronsH

• q charge o" each carrier

• time "or all the charge in the &olume to cross the area at the end o"

the segment[

+ t = l

v

)-



• l distance to tra&el

• & &elocit'

• current is there"ore=

$ = + 6

+ t =|3|n.

v =|3|n v

• & &elocit'

• n densit' o" conduction electrons GN(7[ N number !articlesH

• 7 &olume

• q charge o" carrier

• current is related to the number densit' o" charge carriers and ho/

"ast the' tra&el on a&erage

• 'rift 5elocity J s!eed o" the charge carrier mo&ement

• !o/er su!!l' gi&es the electrons energ' to mo&e

2:. irect 5ersus Alternating Current

• ;$ J alternating current

• D$ J direct current

2:.7 Circuits an' Circuit iagrams

• /lectric current J closed !ath through /hich charge ma' o/

• Electric current !ath com!osed o" a combination o" conductors and

com!onents such as resistors8 ca!acitors or batteries• $ircuits re!resented b' circuit diagrams

2:.6 Po$er &ources

• Capacitors T/o !arallel !lates8 charge o" W and JW

> 9n the region bet/een the !lates there is an electric ?eld> otential di<erence e6ists bet/een the !lates> 9" !lates /ere connected b' a conducting /ire8 the charge /ould

mo&e "rom one !late to the other> This is a circuit o" sorts> $harges /ould e&entuall' sto! mo&ing as electric ?eld got

smaller and smaller

• 9n most electric circuits. De&ice e6ists to maintain !otential

di<erence bet/een the t/o !lates8 so o/ can be continuous

• This is the role o" a batter' in a circuit

• attery 3 maintains a s!eci?c !otential di<erence bet/een t/o

!oints

• $harged !articles can mo&e under the inuence o" an electric ?eld

)



• Field does /or, on the charges8 some e6ternal energ' source

needed to maintain this ?eld

• /lectromoti5e force *emf+ * +J /or, done !er unit charge b'

non>electrical "orces. #easured in 7olts and is not actuall' a "orce.

For a gi&en de&ice8 the net em" is the energ' gained !er unit chargeGC(WH /hen a charge C !asses through that de&ice and gains energ'

C. Sources o" energ' ma' include=> Electrochemical reactions GbatteriesH> adiant energ' Gsolar cellH> Thermal energ' Gthermocou!leH

• ur!ose o" a !o/er source is to !ro&ide energ' to mo&e charges

• Po$er source 3 !roduces a !otential di<erence bet/een t/o

!oints in a circuit8 cause charges to mo&e

2-.: @esistance an' Hhm>s %a$• Hhm>s %a$ - For man' materials there is a linear relationshi!

bet/een the !otential di<erence across a material and the current

o/ through the obIect made o" the same material

• /lectrical resistance *@+

8=.

$

• 7 !otential di<erence bet/een the ends o" the obIect

• 9 current o/ing through obIect

• @ 3 o!!osition to o/ o" electrical current through an obIect8 causes

electrical energ' to be con&erted to heat

• @esistor J obIect that does the abo&e. #easured in ohms J

• #on-ohmic J 9 is not !ro!ortional to 7

2:.; @esistors an' @esisti5ity

• @esistor 3 circuit de&ice that has resistance . = $8

• @esistance 3 in&ersel' !ro!ortional to cross>sectional area

8= & l

"

• l length o" the resistor

• ; cross>sectional area

• resisti&it' o" a material GmH

• good conductor8 lo/ resisti&it'

):



• !utting resistors in series /ill increase resistance

• !utting resistors in !arallel /ill decrease o&erall resistance

Gincreasing area through /hich current can o/H

• KirchoI>s %a$ 3 basic !rinci!le o" D$ circuits Ge6amines e<ect o" a

combination o" resistorsH

2:.E 8ires

• 9n circuits8 elements coneccted b' /ires

• ur!ose to connect t/o !oints in a circuit /ith as little resistance to

current o/ as !ossible

• ;ll !arts o" the circuit connected b' onl' /ire are at the same

!otential. 5ecause adding or remo&ing some /ire "rom a circuit

diagram doesnt ha&e signi?cant e<ect8 as long as the correct

arrangement o" series and !arallel elements is maintained.

• +ires do ha&e small amount o" resistance8 some !otential dro!along them and some energ' lost in the "orm o" heat

2:.10 KirchoI>s %a$

KirchoI>s %a$ of Voltages

• la/ o" energ' conser&ation a!!lied to a circuit

• the sum of the 'irecte' potential 'iIerences aroun' any

close' circuit loop is ?ero• irecte' potential 'iIerence J direction around closed loo! must

be chosen and all !otential di<erences must be e&aluated /ith

res!ect to direction

• @esistance rule J mo&ing through s resistor in the direction o"

current8 change in !otential is 3D@ and in o!!osite direction WD@

• /!" @ule 3 mo&ing through a source o" em"8 the change in

!otential is if going 35e teminal to W5e terminal or > if

going W5e to 35e.

-0



KirchoI>s %a$ of Currents

• a/ o" charge conser&ation

a!!lied to a circuit

• Dn any electrical circuit

$here no buil' up of

charge is occurring sum

of electric currents

Mo$ing into a point

euals sum of the

electric currents Mo$ing

a$ay

2:.11 @esistors in &eries an'Parallel

@esistors in &eries

• @s 3 resistors in series

8s= 81+ 82+ 8, 5

@esistors Parallel

• @p 3 resistors !arallel

1

8 p

=1

81

+1

82

+1

82

5

-1



2:.12 Po$er issipation

• 9n an electrical circuit8 energ' is trans"erred "rom some source and is

used b' other de&ices such as resistors Gthe \loadH

• %oa' 'e5ices J change electrical energ' into other "orms li,e heat8

light and mo&ement

• ate at /hich energ' us mo&ed about is o" more interest than total

amount

• Po$er 3 rate at /hich energ' is !roduced or consumed in circuits

GH G+attsH

P= + E

+ t

• RE /or, done one charges energ' dissi!ated b' load• Rt time

• $urrent o/ing bet/een t/o !oints in a circuit is a measure o" ho/

much charge !asses gi&en !oint each second

$ =6

t

• Di<erence in electrical !otential energ' bet/een these t/o !oints is=

+ 7 =6.

• W charge mo&ed "rom one !oint to the ne6t

• 7 !otential di<erence bet/een the !oints

• 9" !o/er is the change o" energ' !er unit time=

P=6.

t =.$

• o/er dissi!ated b' a resistor is=

P=.$ =.

2

8 = $

2 8

2:.1 Alternati5e /nergy Fnits

1 98h Q 1000Xs-1 x 600s Q 600000 X

-2



98h 3 amount o" energ' used b' 1,+ load in one hour

2:.1 /lectric &hoc9 =a?ar's

• /hen electric current !asses through an' material /ith resistance to

o/ o" current8 energ' dissi!ates in the "orm o" heat• tetanus 3 in&oluntar' muscle contraction

• 5entricular Lbralation 3 e<ect o" electric current on heart8 e<ects

cells

-3



2:.17 /lectricity in Cells

Cell !embrane

• signals sent along ner&e cells are electrical

• signals bet/een cells are chemical• membrane o" cell "ormed "rom t/o la'ers o" !hos!holi!id molecules

• !hos!holi!id biola'ers good insulators8 conductance !er unit area is=

1610>13 >1 m>2

• cell membrane can maintain a se!aration o" !ositi&e and negati&e

charges J has a ca!acitance G1610>2Fm>2H

• resting membrane potential 3 /hen ner&e cell is inacti&e8 an

electrical !otential gradient emits across membrane8 -0>:0m7

• action !otential J ner&e cell becomes acti&e8 !olarit' o" the charge

across membrane changes• outside o" the cell is !ositi&e /ith res!ect

to interior

Circuit !o'els of the Cell an' the Cell

!embrane

• cell membrane can be modelled as a

combination o" dri&ing !otentials8 resistors

and a ca!acitor

• current > combination o" the mo&ement

o" Na ions8 K ions _ $l> ions and8membrane !otential G7mH is the !otential

di<erence this creates bet/een the interior and e6terior o" the cell

• conductance G%H is the reci!rocal o" resistance=

$ =9.

• "orce on an ion /ill de!end on the equilibrium !otential "or the ion

GEionH and the membrane !otential=

$ ion=9ion (. m− Eion)

-4



• &elocit' at

/hich a signal

can mo&e

along such a cell

de!endson the

relationshi! bet/een the resistance across the membrane and the

a6ial resistance along the ner&e cell as /ell as the ca!acitance

• higher resistance lo/er ca!acitance higher s!eed

• to allo/ "ast signal conductance8 either a reduced resistance along

the a6on or an increased membrane resistance is desirable

• lo/er a6ial resistance can be achie&ed b' /ith larger diameter

a6ons

Key Concepts

/lectromoti5e force *emf+* H 3 The /or, done !er unit charge b' non>

electrical "orces. 9t is gi&en the s'mbol and is measured in &olts. The

source o" the energ' can be electrochemical reactions8 magnetic8 thermal

or radiant energ'.

/arth)groun' J 9n electrical circuits8 &oltages are t'!icall' measured

relati&e to a !oint that is considered to ha&e Aero !otential8 ,no/n as the

ground or earth. This is o"ten a direct !h'sical connection to the earth.

Circuit 3 %enerall'8 a closed !ath through /hich current can o/8 is

com!osed o" some combination o" conductors and other com!onents such

as ca!acitors8 resistors or batteries.

Circuit element J a single com!onent o" an electrical circuit8 such as a

resistor or ca!acitor.

irect current *C+ J Electric current that o/s in one direction onl'.

Alternating Current *AC+ J Electric current that re&erses direction

!eriodicall'8 usuall' man' times a second.

Charge Carrier J ; !article carr'ing an electric charge /hich is "ree to

mo&e in res!onse to an electric ?eld8 such as an electron or ion.

/lectrical @esistance *@+ J The o!!osition to o/ o" an electric current

through a material. Electrical resistance causes electrical energ' to be

-*



con&erted to other "orms such as thermal energ'. esistance is measured

in units o" ohms GH.

Hhm>s %a$ J The relationshi! bet/een direct current8 electrical

resistance and a!!lied &oltage across a circuit element. The o/ o" direct

current through a circuit element is !ro!ortional to the a!!lied &oltage.

The constant o" !ro!ortionalit' is called the resistance.

@esisti5ity *G+ J ; tendenc' o" a material to o!!ose the o/ o" electrical

current. The resisti&it' has the s'mbol and is measured in m.

KirchoI>s %a$ of currents 3 9n an' electrical circuit /here no build u!

o" charge is occurring8 the sum o" the electric currents o/ing into a !oint

equals the sum o" electric currents o/ing a/a'. This is consequence o"

charge conser&ation.

KirchoI>s %a$ of 5oltages 3 The sum o" the directed !otential

di<erence around an' closed loo! is Aero. This is a consequence o" the

conser&ation o" energ'.

/lectrical po$er *P+ J The rate at /hich energ' is trans"erred8 dissi!ated

or absorbed b' a circuit element.

@esistors in series 3 T/o or more resistors are in series i" electrical

current goes through them sequentiall'.

@esistors in parallel J T/o resistors are in !arallel i" the circuit branches

s!litting the current such that each resistor has the same !otential

di<erence across it and the circuit subsequentl' reIoins so the current

recombines also.

-)



2;.0 (ime beha5iour of @C Circuits

2;.2 (he @C Circuit

• @C Circuit 3 contain combination o" resistors and ca!acitors• Capacitor J de&ice /hich stores electrical !otential energ' in the

"orm o" a se!aration o" some charge

• Em" ma6imum !otential di<erence in a charged ca!acitor

• $harging o" a ca!acitor ta,es greater or lesser time de!ending on

both the ca!acitance o" the ca!acitor and the resistance o" the

resistor

• +hen ca!acitor is "ull' charged and connected in series /ith Iust a

resistor8 the charge o/s o< the ca!acitor o&er time !eriod /hich

de!ends on the siAe o" _ $

2;. ischarging @C Circuit

• otential di<erence across resistor de!ends on the electric ?eld due

to charge built u! on the ca!acitor !lates

• This /ill change as the ca!acitor discharges current /ill change

o&er time

• %reatest current /ill o/ /hen the ca!acitor is "ull' charged Gand

!otential di<erence is highestH

• $urrent decreases as ca!acitor discharges

+ . capacitor+ + . resistor=0

• R7 !otential dro!s

• otential di<erence across the ca!acitor is related to $ _ q

3=4 + . capacitor

3

4 − $8=0

• $urrent at an' gi&en time is related to change in charge lea&ing

ca!acitor

$ = + 3

+ t

--



+ 3

+ t =

3

84

$ (t )= $ o e−t

:

• characteristic time

• 9n this circuit8 &oltage across ca!acitor is the same as the &oltage

across the resistor GKircho<s a/H

• The discharging ca!acitor8 the &oltage8 current and charge are all

e6!onentiall' deca'ing /ith time

• 7oltage across the resistor series /. ca!acitor is also deca'ing

2;. Charing @C Circuit

• Sum o" !otential di<erence no/ becomes=

+. /atter+ +. capacitor+ +. resistor=0

;− $8− 3

4 =0

• $hange in charge on the ca!acitor !lates is determined b' the

current o/ing onto the ca!acitor !lates

3 ( t )=3 f (1−e

−t

: )

: = 84

• Final amount o" charge is

3 f =4 ℇ

• +ith time8 the charge on the !lates gets closer and closer to a ?nal

&alue

• $urrent o/ing around the circuit must dro! o< to Aero again /hen

the ca!acitor is "ull' charged8 and &oltage across resistor gets less

and less

-



$ (t )= $ o e−t

:

Key Concepts

@C Circuit J ; circuit containing a combination o" ca!acitors G$H andresistors GH.

@C time constant *Y+ J The characteristic time o" an $ circuit. 9n a time

equal to one time constant8 an initiall' uncharged ca!acitor /ill charge to

)3 o" its ma6imum charge and &oltage and current o/ing through the

ca!acitor /ill dro! to 3- o" initial &alue.

-:



2E.0 (he #ature of %ight

2E.2 /lectromagnetic 8a5es

• T/o /a's energ' can be transmitted "rom !lace to !lace> BbIect !h'sicall' mo&es Gtransmission b' !articleH> Energ' is sent as a disturbance through some medium

Gtransmission b' /a&eH

• Photon mo'el of light J light is regarded as a stream o" !article>

li,e units /hich ha&e /a&e !ro!erties

• 8a5e mo'el J light is an electromagnetic /a&e8 that is8 light is a

sel">!ro!agating combination o" oscillating electric and magnetic

?elds

• $hanging an electric ?eld causes a changing magnetic ?eld and

&ice>&ersa

• \/a&ing electric ?elds cause a similarl' /a&ing magnetic ?eld at

right angles to it and these GsinusoidalH oscillating ?elds tra&el

through s!ace at a ?6ed s!eed Gcs!eed o" lightH

(he constant spee' of light

• ight is a sel">!ro!agating /a&e due to being an electromagnetic

/a&e

• Bscillations o" the electric ?eld causes the oscillations o" the

magnetic ?eld• 9t is the relationshi! bet/een the magnetic and electric ?elds /hich

connect the s!atiall' se!arate !arts o" the /a&e

• 9s not a disturbance o" medium

• Sel">su!!orting !rocess onl' !ossible /hen the electromagnetic and

electric /a&es !ro!agate at certain s!eeds

• $ 2.::-:24*610ms>1 Gor 3610>ms>1H

8a5elength an' freuency

• The rate o" the oscillations is the "requenc' o" a /a&e G"H

• Frequenc' is related to /a&elength G&"ZH G&cH

• and " are the &acuum /a&elength and "requenc'8 res!ecti&el'

0



2E. @eMection• @eMection J /hen light hits a sur"ace

some bounces bac, o<

• =ighly polishe' metallic surfaces J a

lot o" light bounces bac, o<

• lac9 surface J nearl' all light is

absorbed

• eected light lea&es the sur"ace at the

same angle that the incident light "alls on

it• %a$s of inci'ence J the angle o"

incidence is equal to the angle o" reection

• ;ngles are al/a's measured "rom

the normal to the sur"ace

• Then normal8 the incident ra' and

reected ra' are all co!lanar

• &pecular reMection J /hen light

hits a &er' at reecti&e sur"ace8 all

light coming "rom a single direction lea&es

in a single direction GreectedH

• @ay J line that starts at one !oint and

tra&els o< in one direction to in?nit'

• iIuse reMection J /hen

sur"ace is rougher8 light is reected

in a /ide range o" directions8 so the

reections are "airl' randoml'

orientated

1



2E. @efraction

• @efraction J change in direction o" a light ra' at the inter"ace

bet/een t/o media /hich occurs /hen there is a change in /a&e

s!eed

•

Frequenc' sta's the same but distance bet/een successi&e !ea,schanges

• +a&elength decreases i" s!eed decreases8 increases /hen the

s!eed increases

• 9" ra' meets the sur"ace along the normal8 there is no change in

direction

• (otal internal reMection J at an' other angle the ra' is either bent

or does not tra&el into the ne6t medium at all

• Dsotropic me'ia J materials that are uni"orm and ha&e the same

/a&e !ro!agati&e s!eed e&er'/here

• e"racti&e inde6 GnH J ratio o" the s!eed o" light in a &acuum to the

s!eed o" light in the material

n=c

v

• & s!eed o" light /a&e in the material

2



&nell>s %a$

• &nell>s %a$ J relates angle o"

incidence and angle o"

re"raction "or /a&e !ro!agation

at the boundar' bet/een

isotro!ic media

• atio o" the sines o" the angle

ratio o" the /a&e s!eed in

the media in&ersel' related

to the re"racti&e indices

sinθ1

sinθ2

=v1

v2

=n2

n1

• +hen light !asses "rom a region o" lo/er n to a region o" higher n8

the light is bent to/ards the normal8 /hen light !asses "rom a

region o" higher n to a region o" lo/er n8 the light is bent a/a' "rom

the normal

(otal Dnternal @eMection

• (otal internal reMection J the com!lete reection o" an incident

light ra' at a boundar'8 /ith no transmission

•

Bccurs onl' "or /a&es incident on a boundar' /ith a medium /herethe re"raction inde6 is reduced

• Critical angle=

sin θc=n2

n1

• 9" angle o" incidence is larger than the critical angle8 none o" the

/a&e /ill be transmitted through the boundar' and onl' reection

occurs

• Total internal reection utilised in man' o!tical de&ices

• B!tical ?bres use total internal reection to con?ne light to a narro/

glass rod8 allo/ing the light to be transmitted &er' long distances> The main source o" loss is absor!tion in the glass8 rather than

loss through light lea&ing the ?bre

• Total internal reection can ham!er e<orts to see into !arts o" the

e'e

3



4



1.0 (he /ye an' Vision

1.2 (he Parts of the /ye

• %ens and cornea J act together to "ocus incoming light onto theretina Gimage "ormationH

• @etina made mainl' o" collagen

• &clera J rest o" the outer sur"ace o" the e'e G?brous /hite !artH

• Anterior chamber J immediatel' behind the cornea n ?lled /ith a

/ater' salt solution Gaqueous humourH

• Aueous humour J constantl' re!laced and im!ortant "or

su!!l'ing nourishment to the cornea and lens8 neither o" /hich are

connected to blood su!!l'

•

%ens J collection o" trans!arent cells sus!ended in !lace b'sus!ensor' ligaments connected to the ciliary muscle

• Ciliary muscle J allo/s "ocusing o" the e'e

• Dris J slightl' in"ront of lens8 connects

to the sclera and ciliary bod'8 made

u! o" !igmented8 ?brous !art ,no/n

as the stroma

• Pupil J ga! in iris through /hich light

!asses

• u!il a!!ears larger than it is due to

magni?cation b' the cornea

• E6!ansion and contraction o" pupil is

in&oluntar' and occurs in res!onse to

light

• Vitreous humour J ?lls bul, o" the

e'e8 gelatinous8 trans!arent material

Gre"racti&e inde6 close to /aterH

• @etina J co&ers bac, sur"ace o" the

e'e8 tissue thin membrane. $ontains

the light sensiti&e cells that allo/ us to see8 there are t/o t'!es=

*



> @o's= res!onds slo/l' to most o"

the &isible /a&elengths> Cones= res!onds "aster but

selecti&el' to regions o" the &isible

s!ectrum

• !acula J s!ot on the retina8 small

!it /ith the highest concentration

o" cone cells. This area is

res!onsible "or central &ision.

• #aIorit' o" re"racti&e !o/er o" the

e'e is !ro&ided b' the cornea

1.; Alternati5e &tructure an' Placement

"ocusing Ability

• #ethods "or "ocussing images o" obIects at &ar'ing distances

include=> $hanging the !o/er o" the "ocusing !art o" the e'e> $hanging the distance to the light sensing !art

• umans can change their "ocal length b' changing the sha!e o" the

lens

/ye Placement an' "iel' of Vision

• &tereoscopic 5ision J t/o e'es see slightl' di<erent &ie/s o" the

/orld and allo/s distances to be Iudged quite /ell8 e'es both !laced

"or/ard>loo,ing and at "ront o" the head. $o&ers onl' about 10f in

"ront o" us.

1.E Colour Vision

etector (ypes

• uman e'e has t/o di<erent t'!es o" light>sensing !hotorece!tors

in the retina J rods and cones• ods J intensit' sensing8 "ar more numerous

• $ones J colour sensing8 located mainl' in centre o" retina

• ods are res!onsible "or night &ision and !eri!heral &ision8 but ta,e

longer to ada!t to changing light conditions due to their sensiti&it'

)



Colour &cience

-



.0 Atoms an' Atomic Physics

.2 Parts of the Atom

• #ost o" an atom is s!ace• ;tom has no net charge

• #ade o" !rotons8 neutrons and electrons

• Atom J smallest unit o" matter /hich retains the chemical

!ro!erties o" an element

• Chemical element J s!eci?c unique number o" !rotons in the

nucleus

. Hrbitals an' /nergy %e5els

/lectrons• Fundamental or elementar' !articles

• Does not ha&e an' underl'ing substructure

• 5elongs to grou! called le!tons

• 9s a !oint>li,e obIect /ith no s!atial e6tent

• $harge= 1.)02610>1:$

• Positron J anti!article equi&alent8 same mass and charge but

!ositi&el' charged

• B"ten bound to !ositi&el' charged nuclei to "orm atoms and

molecules8 but also e6its as "ree !articles

Hrbitals an' /nergy %e5els

• Hrbital J !ath o" an obIect under the inuence o" a central !article

• /lectron J motion determined b' electrostatic "orce /hich al/a's

!oints to/ards the nucleus o" the atom

• Electron in orbit is in a boun' state to nucleus

• Electron has less energ' /hen it is bound to an atom than /hen it is

"ree

• $onsider !articles in bound states as ha&ing negati&e energies

• /nergy uantisation J ,inetic and !otential energ' o" an electroncan onl' sum to s!eci?c &alues

• Dictates /hich orbitals are !ossible

• Electrons inside atoms ma' e6ist onl' in certain states

• /nergy le5els J o" atom de!end on state o" electrons

• 4roun' state J lo/est energ' state

• /xcite' state J all other states



• @ero energ' le&el !ast /hich the electron is no longer bound but

becomes "ree

/mission an' Absorption &pectra

• +hen an electron is in an atom in an e6cited state8 there is a lo/er

energ' state /hich is allo/ed and &acant8 electron can

s!ontaneousl' ma,e transition to this state b' emitting e6tra energ'

as bundle o" electromagnetic radiation J !hoton Gs!ontaneous

emissionH

• Energ' o" !hoton emitted is the di<erence in energ' bet/een t/o

le&els

• hoton emitted /ith energ' E /ill ha&e a !articular "requenc'

E=hf

• adiation absorbed and emitted in bits

• Energ' and "requenc' !ro!ortional to one another

• h Planc9>s Constant J !ro!ortionalit' constant8 ).)2)610>34 Ls

• emission spectrum J range o" !ossible transitions that electrons in

a !articular t'!e o" atom ma' ma,e corres!onds to s!eci?c

"requencies o" electromagnetic radiation

• absorption spectrum J obtained b' measuring "requencies at

/hich collection o" atoms absorb radiation

•

s!ectrum emitted or absorbed de!ends on the number andarrangement o" electrons around the atomic nucleus

:



.0 (he #ucleus an' #uclear Physics

.2 #uclei an' Dsotopes

Protons an' #eutrons

• !rotons and neutrons are not "undamental !articles8 but made u! o"

"undamental !articles called quar,s

• ha'rons J !articles made o" quar,s

• baryons J !articles made o" three quar,s

• nucleons J collecti&el' re"ers to !rotons and neutrons

Atomic #umber

• electron conLguration J electron arrangement into energ' le&els

• chemical !ro!erties determined b' electron con?guration8 thus8chemical !ro!erties de!end entirel' on number o" !rotons in

nucleus

• atomic number J number o" !rotons in nucleus

• atomic mass J number o" !rotons and neutrons

&ymbols an' (erminology

< = "

• @ atomic number Gno. !rotonsH• ; atomic mass G!rotons neutronsH

• m G < = "m

H indicates nucleus is e6cited8 not in lo/est energ'

states8 metastable state

• nucleon J nuclear constituent8 either !roton or neutron

• nucli'e J nucleus or atom /ith s!eci?c nuclear ma,e>u!

• isotopes J atom same number o" !rotons di<erent number o"

neutrons

• isotones J same number o" neutrons8 di<erent number o" !rotons

• isobars J same number o" nucleons8 di<. no o" !rotons G; doesnt

change but @ doesH

• isomers J di<erent nuclear energ' states8 same number o" !rotons

and same number o" neutrons

:0



. /nergy an' !ass Fnits

/ui5alence of !ass an' /nergy

• energ' and mass related b'=

E=mc2

• c 3610ms>1

(he /lectron Volt

• gra&it' not normall' an im!ortant "actor in atomic !h'sics

• use electrostatic !otential energ' instead o" gra&it'

• electron 5olt *eV+ 3 an electron &olt is the electrostatic !otential

energ' o" an electron /hen it is mo&ed through a !otential

di<erence o" 17• modi?ed lanc,s $onstant= ).*610>1)e7s

1 e7 e 6 G17H G1.)02610>1:$H 6 G17H 1.)02610>1: L

(he Atomic !ass Fnit

• mass o" an atom ` 10>2-,g

• atomic mass unit GamuH= 1 amu 1.))1610>2-,g

• #a ;&ogadros number8 number o" atoms in 0.12,g o" carbon

).02261023!er mole

• Atomic !ass G;H mass o" an atom• @elati5e Atomic !ass a&erage atomic mass8 /eighted b'

isoto!e abundance Gdimensionless quantit'H

• !olar mass)gram atomic mass J mass o" 1 mole o" a substance

. #uclear "orces

• Four ,no/n "undamental "orces=> %ra&it'> electromagnetic "orces> /ea, nuclear "orces

> Strong nuclear "orces

(he &trong "orce an' the #ucleus

• Strong nuclear "orce J acts bet/een !roton>!roton8 neutron>neutron8

and !roton>neutron

• No di<erence in strength

• ;cts on the sur"ace o" nucleons8 holds them together

:1



• &#" J strong enough to o&ercome re!elling electrostatic "orce

bet/een !rotons8 creates stable nuclei

• @a'ioacti5e nucli'es J re!ulsi&e electrostatic "orces large enough

to ma,e nucleus unstable8 brea, a!art or change the number o" !

and n to a more stable con?guration

(he 8ea9 #uclear "orce

• es!onsible "or nuclear deca' GQH

• Not in&estigated in this boo,

:2



7.0 Pro'uction of Donising @a'iation

7.1 intro'uction

• roduced either b'=> ;cceleration o" charged !article> adioacti&e deca'

• #uclear of ra'ioacti5e 'ecay process J s!ontaneous change as

a result o" an initiall' unstable nucleus

• ;l!ha GH8 beta GQH and gamma GH deca'

7.2 #uclear ecay Process

• Cnstable nucleus trans"orms into a more stable nucleus8 termed

nuclear 'ecay8 energetic !articles or electromagnetic radiation are

emitted

Alpha ecay

• Cnstable nuclei become more stable b' eIecting t/o neutrons and

t/o !rotons in an as'mmetric s!ontaneous ?ssion !rocess

• Emitted !article bound together as a highl' stable Z particle

• Denoted or >e24 +2

8 as identical to the nucleus o" a helium atom

• $ommonl' seen in large nuclei

• Emitting an al!ha !article is one /a' to increase stabilit' b'

reducing the amount o" !ositi&e charge

%eneral deca' !rocess= < = "

? @ = −2 "−4 + ∝2

4

•

• Daughter nucleus !roduced in al!ha deca' o"ten either in an e6cited

state or still unstable

• E6cited nuclear state J de>e6cite b' gamma radiation

• Still unstable J deca' "urther b' al!ha or beta emission

eta ecay

• Three se!arate !rocesses=- [- 'ecay- [W 'ecay- electron capture

• daughter nucleus o"ten still unstable and Q deca' "ollo/ed ra!idl'

b' gamma emission or another deca' !rocess

:3



• [ 'ecay J does not change the number o" nucleons in the nucleus8

!roduct _ !arents are isobars Gsame number o" nucleons8 di<. no o"

!rotonsH

:4



β- Decay

• \beta minus

• neutron 'ecays proton create'8 accom!anied b' emission o" a

[-

particle and an antineutrino * v́

e+•

v́e J anti!article o" a neutrino8 antimatter !article

• [- > Iust an electron

• !rocess mediated b' a /ea, nuclear "orce

−¿+ v́

+¿+e¿

n ? p¿ e

• !rocess occurs inside the nucleus• atomic mass sta's the same but atomic number increases b' one

< = "

? @ = +1 " + '−1

0 +v́e

• can ha!!en outside the nucleus8 lone neutron

β+ Decay

• \beta !lus

• con&ersion o" !roton to neutron

• energ' is required "or !rocess

• onl' ha!!ens inside nucleus

• a !roton in nucleus deca's8 creating a neutron8 a Q !article and a

neutrino

• [W > anti!article o" an electron8 also !ositron8 e

+¿+v e

+¿? n0+e

¿

energ+ p¿

< = "

? @ = −1 " + '+1

0 +ve

Electron Capture

• re&erse o" Q> Deca'

• nuclear !roton ca!tures an orbiting electron and trans"orms into a

neutron

:*



• alternati&e to Q Deca'8 also results in a !roton j neutron

con&ersion8 but di<erent route

−¿? @ = −1 " +ve

< =

"

+e¿

4amma ecay

• nucleus in an e6cited state can transition to a lo/er>energ' state b'

emitting a !hoton

• !hotons emitted in this !rocess are much more energ' than their

counter !arts in atomic transitions due to much greater energies

in&ol&ed in holding nucleus together

• gamma radiation J high energ' !hotons GH

< = " ¿

? < = "

+- (+- +5)

• k > nucleus in an e6cited state Gor < = "m

long li&ed or metastable

e6cited stateH

• ;n' number o" !hotons ma' be emitted due to a chain o" de>

e6citations occurring as a single e6cited nucleus deca's to its

lo/est>energ' trans?guration

7. Acti5ity an' =alf-%ife

Acti5ity

• Nuclear deca' is random

• o/e&er8 /e can !redict the

!robabilit' that a nucleus /ill

deca' /ithin a gi&en time !eriod

• The theor' o" radioacti&e deca'

de!ends on one "act= (he

number of atoms $hich

'ecay in a gi5en perio' of

time is proportional to the

number of atoms present at

the beginning

+ N

+ t =− #N

:)



• N number o" nuclei o" a !articular t'!e in original sam!le

• RN change in the number o" nuclei !resent a"ter a gi&en time8 R

• Negati&e because number decreases /ith time

•

|

+ N

+ t

| time rate o" change o" the number o" nuclei8 number o"

nuclei /hich deca' in each time !eriod

• B deca' constant

• acti5ity *A+ 3 number o" nuclei /hich deca' in a gi&en time !eriod

"= #N

• small 'ecay constant J sam!le /ith high acti&it' ma' ha&e a

large number o" moderatel' unstable nuclei

• large 'ecay constant J sam!le /ith high acti&it' ma' ha&e asmall number o" highl' unstable nuclei

• &D unit of acti5ity J 5ecquerel G5qH

• 5q equi&alent to one disintegration !er second

• ;s /ell as 5q8 curie $i

• 1 $i 3.-610105q

=alf %ife

N (t )= N 0e− #t

• N0 J number o" radioacti&e nuclei deca' !resent at time t 0

• Z J deca' constant

• NGtH number o" nuclei remaining as a "unction o" time

• #ulti!l'ing both sides o" equation b' Z8 obtain e6!ression "or ;=

" (t )= "0 e− #t

• NGtH tells us the number o" radioacti&e nuclei remaining at time t8 so

i" /e started /ith N08 the number o" nuclei /hich ha&e deca'ed a"ter

time8 t8 is=

N decaed (t )= N 0− N (t )= N 0 (1−e− #t )

• The !robabilit' that a nucleus /ill deca' in a time t is the number

/hich deca' di&ided the number /hich /e started o< /ith8 this tells

us that !robabilit' o" nucleus deca'ing in time t8 is (1−e− #t )

:-



• =alf-life *(1)2+ 3 the length o" time it ta,es "or hal" the number o" a

sam!le o" identical unstable nuclei to deca'

T 12

=ln2

#

• #ean li"e Ganother time scale used in e6!onentiall'>deca'ing

s'stemsH=

: =1

#

!ost %i9ely ecay !o'e an' /xamples of ecay &eries

• $an be !redicted "rom an unstable nucleis com!osition

• Three main regions=> Nuclei belo/ stable region= ha&e too man' neutrons so Q> is most

li,el' deca' !rocess> Nuclei abo&e stable region= ha&e too "e/ neutrons so Q is most

li,el' deca' !rocess or electron ca!ture> Nuclei /ith masses P20 amu are too big and /ill most li,el'

deca' &ia al!ha !article emission

• 9n nature three main chains o" deca' J deca' series

• Deca' series J nucleus that is "ar "rom stable region can undergo a

sequence o" deca's that e&entuall' result in a stable nucleus

7. \-ray Pro'uction

• >ra's are electromagnetic radiation /ith /a&elengths belo/ about

11nm

• roduction is an atomic !rocess not nuclear

• 2 ,e' !rocesses to generate 6>ra's=

> Electron transition into inner shells> Deceleration o" "ast mo&ing "ree electrons

• /lectron transition J can onl' !roduce certain discrete 6>ra'

energies8 6>ra's created this /a' are ,no/n as characteristic raysor characteristic ra'iation. Energies !roduced in these transitions

are characteristic o" a !articular atom

:



• remsstrahlung J !rocess8 "ast>

mo&ing charged !articles are

decelerated and lose ,inetic

energ'8 this lost energ' can be

emitted in the "orm o" electromagnetic radiation

remsstrahlung

• Fast mo&ing electron tra&els

through a material8 interaction

/ith the electric ?elds !roduced

b' local nuclei in the material can

deect the electron "rom its straight

line !ath

• ;mounts in an acceleration o" the

electron "orce has been e6erted on

the electron8 /or, done on it ,inetic

energ' /ill change

• %enerall' their deection /ill slo/ the

electron do/n and thus it /ill continue

to lose ,inetic energ' as it tra&els through the material

• This electron emits the energ' it loses as a !hoton Geg. Emits

electromagnetic radiationH

• This t'!e o" radiation is ,no/n as 5remsstrahlung• There is a ma6imum amount o" energ' an electron can lose8

determined b' initial ,inetic energ' o" the electron

• Electrons are accelerated b' a large !otential di<erence

• #a6 KE is a "unction o" the electric ?eld8 ?6ed onl' b' a!!lied

&oltage

KE=3.

• 9" all this energ' is gi&en u! at once8 then the !hoton /ill ha&e this

much energ'=

h f max=3.

• #a6imum "requenc' !roduced b' 5remsstrahlung "or an

accelerating !article is=

::



f max=3.

h

• h lanc,s constant

•minimum /a&elength is=

#min= hc

3.

• characteristic 6>ra's !roduced b' an 6>ra' tube de!end on the t'!e

o" metal in the target /hich the accelerated electrons stri,e

• accelerating &oltage /ill determine /hich characteristic 6>ra's ma'

be generated

\-ray (ubes

Crookes Tube

• e&acuated glass tube and electronic setu!

• contains gas at lo/ !ressure and has t/o built in electrodes

• anode> !ositi&e

• cathode J negati&e

• /hen &oltage a!!lied is high enough8 s!8e o" the gas ionises

• !ositi&e ions accelerate to/ards cathode and /hen the' stri,e8

liberate electrons

• electrons created accelerate to/ards anode

• i" anode is not bloc,ing the !ath o" e>8 then these e> /ill o&ershoot

and collide /ith glass end o" tube GtargetH

• /ith sucientl' high enough &oltage bet/een electrodes8 these

electrons /ill !roduce 6>ra's

Termionic Tube

• heated ?lament use d to

!roduced electrons

•?lament is heated to a !oint/here e> gain enough energ' to

lea&e the metal and "orm a cloud

or s!ace charge around ?lament

• electric ?eld is used to

accelerate these e> to/ards a

target material Gcommonl'

tungstenH /hich also acts as an anode

100



• accelerated electrons collide /ith anode and !roduce 6>ra's either

b' bremsstrahlung or b' causing emission o" characteristic 6>ra's

7.7 Hther &ources of @a'iation

Pair Annihilation

• /hen a !article and its anti!article meet8 the' annihilate each other8

the energ' equi&alent o" their masses is released as energ' in the

"orm o" !hotons

• all conser&ation la/s are obe'ed

• energ' and momentum also conser&ed

• gamma !hoton !roduced has energ' equi&alent to the total mass o"

the !article>anti!article !air

• to conser&e total momentum8 t/o !hotons o" equal energ' 8

tra&elling in roughl' o!!osite directions8 must be created

• 0.*11#e7 "or electron>!ositron annihilation

Key Concepts

Donising ra'iation J !articles or electromagnetic /a&es /hich ha&e

sucient energ' to ionise atoms and molecules

\-rays J a t'!e o" ionising electromagnetic radiation /ith /a&elengths

"rom about 0.01nm to around 10nm. The lo/ energ' end o" the 6>ra'

s!ectrum o&erla!s /ith the e6treme ultra&iolet

remsstrahlung J the continuum 6>ra' radiation !roduced b' the

brea,ing o" "ast>mo&ing electrons /hen the' interact /ith matter

Characteristic rays J the 6>ra' !hotons !roduced b' electronic

transitions to tightl' bound inner shell orbitals. Transition occurs a"ter the

remo&al o" an inner shell electron8 usuall' b' the collision o" an e6ternall'

!roduced "ast electron. hoton energies !roduced are characteristic o" the

target atom

Annihilation J !rocess in /hich a !article meets its anti!article and both

!articles cease to e6ist8 their mass energ' being con&erted to gamma

radiation. e&erse !rocess is !air !roduction

/lectron #eutrino *5e+ J an elementar' !article !roduced in some

nuclear !rocesses that tra&els at close s!eed o" light and has Aero charge.

101



The mass is not ,no/n8 but the u!!er limit o" the !ossible mass range is

&er' small

Antimatter J most "undamental !articles ha&e an anti!article equi&alent

/ith the same mass and o!!osite charge. +hen a !article and its

anti!article meet8 annihilation occurs.

Alpha ecay J the emission o" a helium>4 !article "rom a larger8 unstable

nucleus8 lea&ing a daughter nucleus that has t/o "e/er !rotons and t/o

"e/er electrons

eta ecay J one o" three di<erent !rocesses that result in a change in

nuclear com!osition but not nucleon number. ; neutron is con&erted into

a !roton and &ice &ersa8 /ith the accom!an'ing created o" a !ositron8 or

the creational(loss o" an electron and the !roduction o" a neutrino or

antineutrino

4amma ecay J a nucleus in an e6cited state can emit energ' as a

!hoton o" electromagnetic radiation8 ,no/n as a gamma !hoton

=alf-life *(1)2+ J The time ta,en "or hal" the unstable !articles in a !ure

sam!le to deca'. ;lso the time ta,en "or the acti&it' o" a sam!le to hal&e

Acti5ity J the measure o" rate o" deca' o" a radioacti&e sam!le. S9 unit "or

acti&it' is 5ecquerel G5qH8 /ith 1 5q equi&alent to one deca' !er second

ecay Constant *B+ J "or an e6!onential deca' !rocess8 the rate at

/hich the quantit' decreases8 is !ro!ortional to the quantit'8 /ith the

constant o" !ro!ortionalit' being the deca' constant

/xponential J ; quantit' is said to change e6!onentiall' /hen the rate o"

change o" that quantit' i" !ro!ortional to the original &alue o" that

quantit'

102



26.0 Dnteraction of Donising @a'iation

6.2 Attenuation of \-rays an' Cross &ection

• Attenuate' J /hen a beam o" radiation o" an' t'!e enters matter itis normall' attenuated8 amount o" energ' in the beam decreases

/ith distance in the material

• The intensit' o" a beam o" !articles or !hotons8 all ha&ing the same

energ'8 decreases e6!onentiall' /ith distance on an isotro!ic media

6. \-rays an' 4amma @a'iation

• #ost attenuation o" high>energ' electromagnetic radiation Ggamma

and 6>ra'sH in matter is due to interaction bet/een incoming

!hotons and the orbiting electrons in the target atom• Se&eral interaction mechanisms=

> $om!lete absor!tion o" the energ' o" the !hoton> Compton eIect J !artial absor!tion o" the energ' o" a !hoton8

results in a ne/ lo/er energ' !hoton tra&elling in a di<erent

direction> Photoelectric eIect J ionisation o" atom8 resulting in a "reeing

o" an orbital electron> $reation o" ne/ !articles

• Number o" collisions de!ends on electron densit' o" the material8

high atomic number materials tend to be more attenuating• igher energ' !hotons are more !enetrating

(he Photoelectric /Iect

• rocess in /hich a !hoton is com!letel' absorbed b' a bound

electron8 gi&ing the electron enough energ' to esca!e /hate&er

binding !otential is holding it8 generating a "ree electron called a

!hotoelectron

• De!ends on binding energ' o" electron

• in'ing energy 3 amount o" energ' electron needs to com!letel'

esca!e "rom the binding !otential

• Energ' o" !hoton=

E=hf

• igher "requenc' higher energ'

• 9ncreasing the energ' o" the radiation /ithout changing "requenc'

has the e<ect o" increasing the number o" !hoton stri,ing the

103



materials but does not increase the energ' that each o" these

!hotons has

• ence8 i" the "requenc' o" the light is abo&e the cut>o< "requenc'8

then increasing intensit' o" the incident light /ill increase the

number o" !hotoelectrons emitted• #a6imum ,inetic energ' o" !hotoelectrons de!ends solel' on the

"requenc' o" the incident light and not at all on the intensit' o" this

light

• Cut-oI freuency J belo/ none o" the !hotons absorbed /ill be

able to !ro&ide bound electrons /ith enough energ' to esca!e the

binding !otential

• $ase o" high energ' radiation=> a&e sucient energ' to liberate electrons "rom inner atomic

orbitals

> +hen !hotoelectrons are emitted "rom inner atomic orbitals8resulting &acanc' quic,l' ?lled b' an out shell electron

> This results in the emission o" the energ' di<erence bet/een

these t/o shells as another G6>ra'H !hoton> This resulting !hoton can be emitted in an' direction and has less

energ' than the original incident radiation Gattenuation occurs J

thus energ' o" incident beam has no/ been reducedH

Pair Pro'uction

• Sucientl' high>energ' gamma>ra' !hotons ma' s!ontaneousl'

con&ert into an electron>!ositron !air

• Energ' o" !hoton con&erted into matter and antimatter

• #inimum !hoton energ' necessar' "or the !air !roduction

• Bnl' !hotons /ith "requenc' P2.*61020 A /ill be able to !roduce

electron>!ositron !airs

• ;ll conser&ation la/s must be satis?ed

• e&erse o" this !rocess in !article>anti!article annihilation

• Energ' o" an incoming beam o" gamma radiation /ill be attenuated

i" !air !roduction occurs

•ositron !roduced in this !rocess /ill ultimatel' undergo annihilation/ith an electron /ithin the medium and this /ill !roduce t/o

!hotons Gthese /ill ha&e less energ' than original gamma !hotonH

• rocess o" !air !roduction act to reduce the energ' o" a beam o"

electromagnetic radiation

104



Compton /Iect

• 9nteraction bet/een

electromagnetic radiation and

matter in /hich !hotons dis!la'

their !article li,e nature• igh energ' !hoton is scattered

rather than absorbed b' a !article

• +hen an incoming !hoton is

incident on a nearl' "ree electron

/hich is more or less at rest8

energ' is trans"erred "rom the

!hoton to the electron

• Electron gains ,inetic energ' and

mo&es o< in the same direction

• ; lo/er>energ'8 longer>/a&elength !hoton results

• $hange in /a&elength is related to the angle at /hich the !hoton is

scattered

• +hen $om!ton scattering occurs8 incoming !hoton loses energ' to

the scattering electrons attenuation

6. Particles

#eutrons

• Cncharged8 interact !redominantl' /ith nuclei in attenuating

materials in the "ollo/ing /a's=> /lastic collisions= ,inetic energ' conser&ing collision /ith

another !article> #on-elastic collision= neutron interacts /ith a nucleus and is

re>emitted /ith a di<erent Gnormall' reducedH ,inetic energ'

10*



> Capture= the neutron is ca!tured and becomes !art o" the

nucleus> &pallation)Lssion= neutron is ca!tured b' increase in energ'

causes the nucleus to "ragment. S!allation term "or the

!roduction o" "ragments /hen an obIect is subIected to an im!act

or stress. Fission is the s!litting o" an obIect in t/o !aths

• robabilit' o" a neutron to interact /ith a !article nucleus is energ'

de!endant

• Elastic collisions dominate8 energies O 100,e7

• 9n>elastic collisions more li,el' abo&e a "e/ #e7

• S!allation occurs abo&e 20#e7

Dons

• rotons8 al!ha !articles and hea&' nuclei

• Capture of electrons J energetic incoming ion ca!tures one ormore electrons "rom the absor!tion material and becomes a neutral

atom. 9n this !rocess8 the ion loses ,inetic energ' and ionises the

surrounding material. This occurs "or lo/ energ' radiation

• Collision $ith electrons J energetic incoming ion collides /ith

atoms o" absorbing material. Surrounding material is ionised and the

atoms o" the absorbing material ma' be li"ted into e6cited atomic

states. Energ' to ionise or e6cite surrounding material comes "rom

the incoming ion8 there"ore the incoming ion loses ,inetic energ'.

•

#uclear collision J incoming ion collides directl' /ith the nucleuso" an atom in the absorbing material. Bccurs onl' /hen incoming

ion is at &er' high energ'. rocesses such as ?ssion(s!allation ma'

be induced.

/lectrons)Positrons

• Annihilation J !ositrons ma' collide /ith electrons and be

annihilated

• Collisions $ith atomic electrons J energetic and incoming

electrons ma' collide /ith and eIect electrons "rom &arious atomic

shells8 in the atoms o" absorbing material• remsstrahlung J the deceleration o" energetic electrons and the

subsequent emission o" lost ,inetic energ' as electromagnetic

radiation

• Ceren9o5 ra'iation J electromagnetic radiation emitted /hen

electrons tra&el through a material at s!eeds greater than the s!eed

o" light through that material. This e<ect ma' !roduce ultra&iolet

10)



radiation. Bccurs "or electrons /ith ,inetic energ' abo&e about

*00,e7 /hen tra&elling in /ater

6.7 etection of Donising @a'iation

(he 4eiger-!]ller (ube• %as detector "or the detection o" al!ha and beta radiation

• $an be used "or gamma detection8 ho/e&er8 ecienc' is quite lo/

as gas inside is at quite lo/ !ressure

• 9onising !article !asses through a thin /indo/ at the end o" the tube

and ionises the gas

• $harged !articles that are then created b' an electric ?eld8 and

collide /ith "urther gas !articles8 creating an a&alanche o" charged

!articles

•

This current is detected and recorded as an audible clic, or s!i,e inthe out!ut signal

• $an onl' detect the !resence o" the

radiation and not its energ'

Photomultiplier

• Photomultipliers 3 am!li"' the signal

generated b' the detection o" a !hoton

• /hen !hoton hits a !hotocathode inside a

&acuum tube8 it triggers release o" a

!hotoelectron• this electron is accelerated to/ards nearb'

electrode Gcalled d'nodeH that is at a higher

!otential then the cathode8 /hen it stri,es

the d'node8 more electrons are emitted

• !rocess re!eated u! to se&eral times to

!roduce u! to 10) electrons "rom a single !hoton

• &oltage o" se&eral thousand &olts are t'!icall' required

• can be used as !art o" scintillation counters

•

scintillating material Gone that generates !hotons /hen struc, b'ionising radiationH is used and then these !hotons are con&erted to

electrical !ulses /ith a !hotomulti!lier

• ha&e the ad&antage o" !roducing in"ormation about the energ' o"

the incident !article as the number o" !hotons generated in the

scintillating material is !ro!ortional to the energ'

Photographic /mulsion

• detection ?lm

10-



• >ra's a<ect the ?lm in much the same /a' as &isible light does[

sil&er halide salts are con&erted to metallic sil&er b' incident

!hotons

• Csed "or detection o" 6>ra's in medical diagnostics

•

To im!ro&e the sensiti&it' o" the ?lm and reduce e6!osure needed8?lm is o"ten coated on both sides /ith a uorescent material that

increases the e<ect o" 6>ra's on the ?lm

• Sometimes a la'er o" lead is used under the !hotogra!hic emulsion

to bac,scatter the 6>ra's through the ?lm a second time

Key Concepts

Photoelectric /Iect J The !rocess in /hich electrons are emitted "rom a

material /hen electromagnetic radiation is incident on the sur"ace

Compton /Iect J a !rocess in /hich a !hoton is scattered o< an electronsuch that it undergoes a change in direction and a corres!onding

reduction in "requenc'

Photon !omentum J /hile !hotons ha&e \Aero rest>mass8 the' do carr'

momentum p=

h

#

Pair Pro'uction J the !roduction o" a !article>anti!article !air8 usuall'

"rom energetic gamma !hotons

4eiger-!]ller (ube J ; gas>?lled tube "or detecting and counting

radiation. 9t is most ecient "or al!ha and beta radiation

Photomultiplier> ; light>detection de&ice. 9ncident light !roduces

electron emission b' the !hotoelectric e<ect8 and these electrons are

am!li?ed b' a series o" electrodes at increasing !otentials to !roduce a

detectable current.

&cintillating !aterial J a material8 such as sodium iodide8 that emits a

ash o" light /hen it absorbs ionising radiation. These are o"ten used inconIunction /ith !hotomulti!lier "or radiation detection.

10



:.0 iological /Iects of Donising @a'iation

:.2 !echanisms of Cell amage

• 9onising radiation causes damage to molecules8 occasionall' b'direct hit on a molecule but more o"ten indirectl' b' the creation o"

\"ree radicals

• "ree ra'icals J uncharged atoms or "ragments o" molecules

!ossessing an un!aired electron "ormed b' s'mmetrical brea,ing o"

a co&alent bond

• $ause damage to cellular !roteins b' brea,ing molecular bonds and

rendering !roteins non>"unctional and e&en harm"ul

• Direct hit or "ree>radical !roduction b' radiation ma' damage

cellular DN;=> DN; damage /hich the cell can detect and ?6e> DN; damage to the cell that cannot be ?6ed8 causing a!o!tosis

G"orm o" !rogrammed cell deathH> Non>lethal damage that is !assed on as a mutation in subsequent

cell di&isions

• &omatic #A 'amage J non>inheritable8 serious ad&erse

mutation8 increase the ris, that cancer /ill de&elo!

• %enetic DN; damage J inheritable and results "rom mutation in the

re!roducti&e cells8 ma' then be !assed on to "uture generations

• y-stan'er eIect J neighbouring cells not directl' damaged b'radiation ma' e6!erience damage b' communication /ith the

damaged calls

:. ose an' ose /ui5alent

Absorbe' ose

• Absorbe' 'ose *+ J !h'sical quantit' /hich quanti?es the

amount o" energ' absorbed b' some material

• S9 unit gra' J %' 1 Ioule o" energ' being deli&ered to one ,ilogram

o" matter

• 1 %' 1L(K% 100 rad

A= + E

m

• RE J energ' lost "rom radiation beam

• m J mass o" material beam is entering

10:



• absor!tion dose is a general conce!t

• a!!lies to all ,inds o" radiation and all t'!es o" absorbers

• e<ect o" radiation on a biological tissue de!ends directl' on the

amount o" energ' absorbed b' that tissue

•

amount o" damage !roduced b' radiation is !ro!ortional to theamount o" energ' "rom the radiation that is absorbed

• di<erent t'!es o" ionising radiation lose energ' in matter in di<erent

/a's

ose /ui5alent

• 'ose eui5alent J e6!ression "or the dose in terms o" its biological

e<ect

• relati5e biological eIecti5eness *@/+ J quanti?es the damage

!roduced b' each ,ind o" radiation in biological tissue8 &aries "rom

one ,ind o" radiation to another• distance tra&elled b' a !articular ,ind o" radiation is de!endent on

the rate at /hich that t'!e o" radiation de!osits energ' in matter

• electricall' charged !articles interact strongl' &ia the electroc ?eld

and this de!osit their energ' relati&el' quic,l'

• larger !articles /ill also lose energ' ra!idl' because the' are more

li,el' to collide /ith !articles o" the material through /hich the' are

tra&elling

• al!ha !article has t/ice the charge o" the beta !article and is also

much larger• thus8 energetic al!ha !articles /ill de!osit their ,inetic energ' more

ra!idl' o&er smaller distances than beta !articles /ith the same

initial energ'

• similarl' beta !articles /ill de!osit their ,inetic energ' more ra!idl'

and o&er a smaller distance than gamma ra' !hotons /ith the same

initial energ'

• al!ha !article range is less than that o" beta8 gamma or 6>ra's

results in radiation de!ositing its energ' in a smaller area

• greater concentration o" ionisation and cell damage results in

greater Gad&erseH biological e<ect8 and thus a larger &alue o" 5E

:. (ypes of /Iects

• eterministic ra'iation 'amage J !roduced b' radiation doses

that are high enough to denature !roteins or to cause cell death.

These e<ects are de?nite8 noticeable and "airl' immediate

110



• &tochastic ra'iation 'amage J small radiation dose8 damage

ma' not be ob&ious but ris, o" disease is increased Gconsequences

are !robalisticH. %o&erned b' the cause o" !robabilit'

• $haracteristics o" deterministic e<ects=

> Earl' e<ects8 a!!ear quic,l'> esult o" \lethal damage8 cells o" tissue ,illed b' radiation

e6!osure> Killing o" cells e6tensi&e enough that reduces or destro's at least

some organ "unction> There is a \threshold dose belo/ /hich deterministic e<ects do

not occur> Se&erit' increases /ith dose

• Stochastic e<ects=> ate e<ects8 do not a!!ear immediatel'> $aused b' cellular or DN; damage8 e<ects not immediatel'

lethal> $an result in cellular mutation or abnormal changes in cell

"unction> Bnl' !ossible to estimate the !robabilit' o" harm gi&en a

!articular dose le&el> Se&erit' o" the e<ect is not de!endent on the dose> The !robabilit' o" harm increases /ith increased dose

:.7 !e'ical @is9s an' /Iects

•

@a'iation sic9ness J re"ers to grou! o" deterministic e<ects8obser&ed to a!!ear soon a"ter &er' large radiation doses

• $ells most susce!tible to death "rom radiation are=> 9ntestinal lining> +hite blood cells> $ells that ma,e red and /hite blood cells

• Time ta,en "or a !erson to die "rom a lethal dose o" radiation is 2>4

/ee,s

• atients that recei&e a high "ull>bod' dose o" radiation and are stilla

li&e a"ter ) /ee,s8 are li,el' to reco&er

• robabilit' o" de&elo!ing cancer "rom radiation e6!osure increaseslinearl' /ith the accumulated dose and there is no minimum

threshold o" e6!osure belo/ /hich there is no ris, J %#(

hypothesis *%inear-nothreshol'+

:.6 Fltra5iolet @a'iation

• C7 !hotons are those in /a&elength range bet/een 6>ra's and

&isible light8 10nm to 400nm.

111



• Sun most im!ortant

source o" C7 radiation

Gemits /a&elengths

200nm u!H

•

C7;= 400nm>320nm• C75= 320nm J 20nm

• C7$= 20nm>200nm

• BAone u!!er atmos!here

good absorber o" C8 !racticall' no radiation O300nm reaches sea

le&el in most !laces

• ;ir largel' o!aque at /a&elengths O 200nm due to absor!tion b'

o6'gen

• #ost C7 /ere e6!osed to C7;

• C75 needed "or &itamin D !roduction in bod'

• C7 radiation mostl' not energetic enough to interact /ith an' but

&alence electrons in atoms o" matter it !asses through8 ho/e&er8

can still disru!t biological molecules

• ;ll C7 light reaching Earths sur"ace /ill damage collagen in s,in

!remature aging

• C7; least harm"ul

• C75 can cause DN; damage b' disru!ting co&alent bonds s,in

cancer8 cataracts

• Short /a&elength C7 damage bacteria8 inhibit abilit' to re!licate

• Sunscreen J bloc,ing C7 light Greecting8 titanium dio6ideH orabsorbing and re>radiating at much longer /a&elengths

Ga&obenAone doesH

• The greater the "requenc'8 the greater the energ'

• The greater the /a&elength8 the smaller the "requenc'

;.0 !e'ical Dmaging

;.2 \-ray Dmaging

• >ra' radiogra!h J bod' o" interest in e6!osed to 6>ra's /hile a!hotogra!hic ?lm is !laced beneath the bod'

• roduces an image /here areas o" greater e6!osure corres!ond to

the areas o" the bod' that are the most trans!arent to 6>ra's

• ecords degree o" transmission o" 6>ra's as a shado/ gra!h

• ;ttenuation o" 6>ra' !hotons de!ends on=

112



> hoton energ' Gdetermines /hich t'!e o" interaction occurs J

$om!ton scattering _ !hotoelectric e<ect are dominant

!rocessesH> The atomic number o" ,e' elements !resent in the materials

being imaged

• Photoelectric eIect J !redominant interaction "or lo/ energ'

GO3*,e7H 6>ra' !hotons

• robabilit' o" !hotoelectric e<ect "alls ra!idl' /ith increasing !hoton

energ' G&aries roughl' !ro!ortional to the in&erse o" the energ'

cubedH

• Compton eIect J higher energ' 6>ra's GP30>40,e7H

• robabilit' o" $om!ton e<ect has little de!endence on atomic

number8 but does de!end on electron

densit'

;. C( &can

• $om!uted tomogra!h'

• roduces cross>sectional images

• roIection o" 3D structure onto a 2D ?lm

• $om!uter used to reconstruct a !icture

"rom the transmission data

• Scan in&ol&es an e<ecti&e radiation dose

o" about 2>10mS&

;. P/( &can

• ositron emission !hotogra!h'

• Nucleus undergoes beta !lus deca'8

!ositron is emitted

• ositron anti!article o" electron and

quic,l' collides /ith an electron and

both are annihilated

• roduces t/o !hotons8 each /ith

energ' o" *11,e7

• T/o !hotons are emitted in e&enl'e6actl' o!!osite directions

• $an get in"o on metabolic !rocesses not

Iust structure in"o

• +or,s b' detecting simultaneousl' emitted !airs o" !hotons at

about *11,e7

• imitation is the need "or short li&ed isoto!es that ha&e to be

!roduced in a c'clotron

113



• Detecting simultaneous !hotons allo/s reconstruction o" the

location /here the !ositron /as annihilated

• Dose "rom ET scan similar to $T scan

;.: Fltrasoun' &onography

• Does not use ionising radiation

• Ctilises high "requenc' acoustic &ibrations8 abo&e the limit o" human

hearing GP20,AH

• +hen a /a&e is tra&elling through a medium and it reaches a

boundar' /ith another medium8 some o" the /a&e is transmitted

through the boundar' and some is reected

• 9n case o" sound /a&es8 the amount o" reection de!ends on

acoustic im!edance o" the media J greater the im!edance mismatch

bet/een t/o media8 the more reection o" the ultrasound there /ill

be• ;coustic im!edance de!ends on the s!eed at /hich sound tra&els

through a medium8 this in turn de!ends on the densit' o" material

• 9n order to generate an image in a medical setting8 de&ice called

!ieAoelectric transducer is used to !roduce acoustic /a&es /ith

"requenc' in the lo/ #A range

• +a&es !roduced reected bac, "rom boundaries bet/een tissue

t'!es

• Cltrasound signal emitted in !ulses

•5' detecting the time dela' "or the echo !ulses and the signalstrength8 !icture can be built u! o" location o" boundaries

• 5ecause im!edance bet/een s,in and air is do di<erent8 i" there is

an' air ga! bet/een the s,in and transducer then most o" the

intensit' is lost b' the /a&es being reected be"ore !enetrating the

bod'

• %el can be used bet/een s,in and transducer J im!edance

matching

• Cltrasonogra!h' is generall' considered to be sa"e

• Cltrasound signal consists o" mechanical !ressure /a&es8 /hich can

ha&e a heating e<ect on the tissue

114



E.0 #uclear !agnetic @esonance

E. A brief outline of !@D

• atient !laced in a large magnetic ?eld• Bscillating electromagnetic ?eld is turned on

• Field is oscillating in the radio>"requenc' range o" the

electromagnetic s!ectrum and is tuned to trans"er energ' to the

!rotons /hich are the nuclei o" h'drogen atoms in !atient

• Energ' or F ?eld is absorbed b' the h'drogen nuclei and this

energ' is re>radiated b' these nuclei as another F electromagnetic

?eld

• Second F electromagnetic ?eld is detected b' antennas in the #9

machine and the signal !roduced is anal'sed b' !o/er"ul com!utersto !roduce detailed images

• F ?eld returned b' the !atient contains in"ormation about the

!osition and com!osition in /hich the !rotons reside.

• 9n !articular8 the "requenc' Gand !haseH o" the emitted signal can

indicate /here the signal came "rom and the deca' time gi&es

in"ormation about tissue com!osition

university of queensland phys1171 chapter notes/study notes based on introduction to biological...

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