chapter24 quantum physics

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24. QUANTUM PHYSICS

Liew Sau Poh

Outline

24.1 Photons24.2 Wave-particle duality24.3 Atomic structure24.4 X-rays24.5 Nanoscience

Objectives

(a) describe important observations inphotoelectric emission experiments

(b) recognise features of photoelectric emissionthat cannot be explained by wave theory andexplain these features using the concept ofquantisation of light

(c) use the equation for a photon E = hf (d ) explain the meaning of work function and

threshold frequency

Objectives

(eeffect, hf =W + ½mv2

max

( f ) understand the meaning of stopping potentialand use eV s= ½mv2max

(h) use the relation = h/p to calculate deBroglie wavelength

(i) interpret the electron diffraction pattern as anevidence of the wave nature of electron

Objectives( j) explain the advantages of an electron

microscope as compared to an opticalmicroscope

(l) derive an expression for the radii of the orbits

(m) derive the formula

Objectives(n) explain the production of emission line

spectra with reference to the transitionsbetween energy levels

(o) explain the concepts of excitation energy andionisation energy

(p) interpret X-ray spectra obtained from X-raytubes

(q) explain the characteristic line spectrum and

continuous spectrum including min in X-rays

Objectives

(r) derive and use the equation min = hc / eV

(s) describe X-ray diffraction by two paralleladjacent atomic planes

d sin = m

(u) explain the basic concept of nanoscience(v) state the applications of nanoscience in

electronics devices

24.1 Photon

Photoelectric effect: When electromagnetic radiation is incident tothe surface of a metal, electrons are ejectedfrom the surface.

Photoelectrons:

The electrons emitted by this effect.UV

Metals Metals other than Alkali Metals Alkali Metals

Visible light

No photoelectronsPhotoelectrons Photoelectrons

Visible light



Photon

A packet or bundle of energy is called aphoton.

Energy of a photon is

where h

f is the frequency of the radiation or photon,

c is the speed of light (e.m. wave) and

is the wavelength.

E = hf =hc

m =h

cEc2 =

p =hE

c =

Properties of photons

A photon travels at a speed of light c in vacuum.(i.e. 3 x 108 m/s)

It has zero rest mass. i.e. the photon can not existat rest.

The kinetic mass of a photon is,

The momentum of a photon is,

Photons travel in a straight line.Energy of a photon depends upon frequency of thephoton; so the energy of the photon does notchange when photon travels from one medium toanother.

Properties of photons

Wavelength of the photon changes indifferent media; so, velocity of a photon is

different in different media.Photons are electrically neutral.

Photons may show diffraction under givenconditions.

Photons are not deviated by magnetic andelectric fields.

Metals other than Alkali Metals

Visible lightNo photoelectrons

UV

Metals

Photoelectrons

Alkali Metals

PhotoelectronsVisible light

Photoelectric Effect

Photoelectric EffectThe phenomenon of emission of electrons from mainlymetal surfaces exposed to light energy (X rays,rays, UV rays, Visible light and even Infra Red rays) ofsuitable frequency is known as photoelectric effect.The electrons emitted by this effect are calledphotoelectrons.The current constituted by photoelectrons is known asphotoelectric current.Note: Non metals also show photoelectric effect.Liquids and gases also show this effect but to limitedextent.

Experimental (Photoelectric Effect)

UV light

K V

+A

+

C A

W

C Metallic cathode

A Metallic Anode

W Quartz Window

- Photoelectron


Glass transmits only visible and infra-red lightsbut not UV light.Quartz transmits UV light. When light of suitable frequency falls on themetallic cathode, photoelectrons are emitted.

These photoelectrons are attracted towards the+ve anode and hence photoelectric current isconstituted.

I A

Intensity (L)0


1) Effect of Intensity of Incident Light onPhotoelectric Current:For a fixed frequency, the photoelectric currentincreases linearly with increase in intensity ofincident light.



0

SaturationCurrent

L1

L2

L2 > L1

IA

+Potential of A (V)VS


2) Effect of Potential onPhotoelectric Current:For a fixed frequency andintensity of incident light,the photoelectric currentincreases with increase in+ve potential applied to theanode.

When all thephotoelectrons reach theplate A, current becomesmaximum and is known assaturation current.

0

SaturationCurrent

L1

L2

L2 > L1

IA



2) Effect of Potential onPhotoelectric Current:

When the potential isdecreased, the currentdecreases but does notbecome zero at zeropotential.This shows that even in theabsence of accelerating

potential, a fewphotoelectrons manage toreach the plate on theirown due to their K.E.

0

SaturationCurrent

L1

L2

L2 > L1

I A



2) Effect of Potential onPhotoelectric Current:

When ve potential is

applied to the plate A w.r.t.C, photoelectric currentbecomes zero at aparticular value of vepotential called stoppingpotential or cut-offpotential.Intensity of incident lightdoes not affect the stoppingpotential.

IA

Potential of A (V)0VS1

+

Saturation Current

1

2

2 >

1

VS2


3) Effect of Frequency of IncidentLight on Photoelectric Current:For a fixed intensity of incidentlight, the photoelectric current

does not depend on thefrequency of the incident light.Because, the photoelectriccurrent simply depends on thenumber of photoelectronsemitted and in turn on thenumber of photons incidentand not on the energy ofphotons.

IA


+

Saturation Current

1

2

2 >

1

VS2

Experimental (Photoelectric Effect)4) Effect of Frequency of

Incident Light on StoppingPotential:For a fixed intensity ofincident light, thephotoelectric currentincreases and is saturated

with increase in +vepotential applied to theanode.However, the saturation

current is same fordifferent frequencies of theincident lights.

IA


+

Saturation Current

1

2

2 >

1

VS2

Experimental (Photoelectric Effect)4) Effect of Frequency of

Incident Light on StoppingPotential:

When potential isdecreased and taken belowzero, photoelectric currentdecreases to zero but atdifferent stoppingpotentials for differentfrequencies.

Higher the frequency, higher the stopping potential. i.e. VS

VS (V)

0 0

5) Threshold Frequency

The graph between stoppingpotential and frequency does notpass through the origin.It shows that there is a minimum

value of frequency called thresholdfrequency below which photoelectric

emission is not possible howeverhigh the intensity of incident lightmay be.It depends on the nature of the metalemitting photoelectrons.

28.2 Concept of light quantisation



Laws of Photoelectric Emission

For a given substance, there is a minimum value of frequency of incident light calledthreshold frequency below which nophotoelectric emission is possible, howsoever,the intensity of incident light may be.The number of photoelectrons emitted persecond (i.e. photoelectric current) is directly

proportional to the intensity of incident lightprovided the frequency is above the thresholdfrequency.

Laws of Photoelectric Emission

The maximum kinetic energy of the photoelectrons isdirectly proportional to the frequency provided thefrequency is above the threshold frequency.The maximum kinetic energy of the photoelectrons isindependent of the intensity of the incident light.The process of photoelectric emission isinstantaneous. i.e. as soon as the photon of suitablefrequency falls on the substance, it emitsphotoelectrons.The photoelectric emission is one-to-one. i.e. forevery photon of suitable frequency one electron isemitted.

the energy of the photon is absorbed by the electronand is used in two ways:

A part of energy is used to overcome the surfacebarrier and come out of the metal surface. This part work function 0).

The remaining part of the energy is used in giving a

to the maximum kinetic energy of the photoelectrons( ½ mv 2max

According to law of conservation of energy,

hf = + ½ mv2max

= hf 0 + ½ mv2max

½ mv2max = h ( f - f 0 )

Photon h

Metal

Photoelectron

½ mv2max

= h 0

½ mv2max = h ( - 0 )

Verification of Laws of Photoelectric Emission based

If < 0, then ½ mv 2max is negative, which isnot possible. Therefore, for photoelectricemission to take place > 0.Since one photon emits one electron, so thenumber photoelectrons emitted per second isdirectly proportional to the intensity ofincident light.

½ mv2max = h ( - 0 )

Verification of Laws of Photoelectric Emission based

It is clear that ½ mv 2max as h and 0 are constant.This shows that K.E. of the photoelectrons is directlyproportional to the frequency of the incident light.Photoelectric emission is due to collision between aphoton and an electron. As such there can not be anysignificant time lag between the incidence of photonand emission of photoelectron. i.e. the process is

instantaneous. The delay is only 10-8

seconds.

Application of Photoelectric Effect

Automatic fire alarm

Automatic burglar alarm

Scanners in Televisiontransmission

Reproduction of sound incinema film

In paper industry tomeasure the thickness ofpaper

To locate flaws or holes inthe finished goods

In astronomy

To determine opacity ofsolids and liquids

Automatic switching ofstreet lights

To control thetemperature of furnace

Photometry

Beauty meter Tomeasure the fair

complexion of skinLight meters used incinema industry to checkthe light

Photoelectric sorting

Photo counting

Meteorology

Photoelectric ThresholdBinding Energies

K: 100L: 50M: 20

Photon in

Photon energy: 15

Which shells arecandidates forphotoelectricinteractions?



Photoelectric Threshold

Photon in

Photon energy: 15

NO

NO

NO

Binding EnergiesK: 100L: 50M: 20



Photon in

Photon energy: 25




Photon in

Photon energy: 25

NO

NO

YES

Binding EnergiesK: 100

L: 50M: 20



Photon in

Photon energy: 22

Which photon hasa greaterprobability forphotoelectricinteractions withthe m shell?

Photon energy: 25

A

B

1

P.E. ~ -----------energy3

Binding EnergiesK: 100

L: 50M: 20


Photon in

Photon energy: 55




Photon in

Photon energy: 55


NO

YES

YES



Photon in

Photon energy: 105




Photon energy: 105

YES

YES

YES






Photoelectric interactions

decrease with increasing photonenergy

1P.E. ~ -----------

energy3


Binding EnergiesK: 50L: 25

Photon energy: 49

NO

YES

Photon energy: 51

YES

YES

When photon energy just reaches bindingenergy of next (inner) shell, photoelectricinteraction now possible with that shell

shell offers new candidate target electrons


When photon energies just reaches binding energy of

next (inner) shell, photoelectric interaction now

possible with that shell, where shell offers new

candidate target electrons

Photon Energy

InteractionProbability

K-shellinteractions possible

L-shellinteractions

possibleL-shellbindingenergy

K-shellbindingenergy

M-shellinteractions

possible


causes step increases in interactionprobability as photon energy exceeds shell

binding energies

Photon Energy

InteractionProbability L-edge

K-edge

24.2 Wave-particle Duality

Dual Nature of Radiation and Matter Wave theory of electromagnetic radiationsexplained the phenomenon of interference,diffraction and polarization.On the other hand, quantum theory of e.m.radiations successfully explained thephotoelectric effect, Compton effect, blackbody radiations, X- ray spectra, etc.Thus, radiations have dual nature. i.e. waveand particle nature.

Dual Nature of Radiation and Matter

Louis de Broglie suggested that the particles likeelectrons, protons, neutrons, etc have also dual nature.i.e. they also can have particle as well as wave nature.Note: In no experiment, matter exists both as aparticle and as a wave simultaneously. It is either theone or the other aspect. i.e. The two aspects are

complementary to each other.His suggestion was based on:The nature loves symmetry.The universe is made of particles and radiations andboth entities must be symmetrical.

de Broglie wave

According to de Broglie, a moving materialparticle can be associated with a wave. i.e. a wave can guide the motion of the particle.The waves associated with the moving materialparticles are known as de Broglie waves or

matter waves.



Expression for de Broglie wave

According to quantum theory, the energy of thephoton is

the photon is

If instead of a photon, we have a materialparticle of mass m moving with velocity v, thenthe equation becomes which is the expression for de Broglie wavelength.

E = h =hc

E = mc2

So = hmc

or =hp

where p = mcis momentum of a photon

= hmv

The Compton Effect

Let the light is made up of particles (photons),and that photons have momentum, with energyhf collides with a stationary electron.Some of the energy and momentum istransferred to the electron (this is known as theCompton effect), but both energy and

momentum are conserved (elastic collision). After the collision the photon has energy hf andthe electron has acquired a kinetic energy K .Conservation of energy: hf = hf + K

Conclusionde Broglie wavelength is inversely proportional to the

velocity of the particle. If the particle moves faster,then the wavelength will be smaller and vice versa.

If the particle is at rest, then the de Broglie wavelengthis infinite. Such a wave can not be visualized.de Broglie wavelength is inversely proportional to themass of the particle. The wavelength associated with aheavier particle is smaller than that with a lighterparticle.de Broglie wavelength is independent of the charge ofthe particle.

= hmv

Conclusion

Matter waves, similar to electromagnetic waves,can travel in vacuum and hence they are not

mechanical waves.Matter waves are not electromagnetic wavesbecause they are not produced by acceleratedcharges.Matter waves are probability waves, amplitudeof which gives the probability of existence ofthe particle at the point.

= hmv

Davisson and Germer Experiment A beam of electronsemitted by the electrongun is made to fall onNickel crystal cut alongcubical axis at aparticular angle.The scattered beam ofelectrons is received bythe detector which can berotated at any angle.

F

V

C

A

Nickel Crystal

Electron Gun

Crystal Lattice

Davisson and Germer ExperimentThe energy of theincident beam ofelectrons can be varied bychanging the applied

voltage to the electrongun.Intensity of scatteredbeam of electrons isfound to be maximum

when angle of scatteringis 50° and the

accelerating potential is54 V.

F

V

C

A

Nickel Crystal

Electron Gun

Crystal Lattice

Davisson and Germer Experiment

+ 50° + = 180°

i.e. = 65°

For Ni crystal, latticespacing d = 0.91 Å

For first principalmaximum, n = 1

Electron diffraction issimilar to X-raydiffraction.

F

V

CA

Nickel Crystal

Electron Gun

Crystal Lattice

2dsin = n gives = 1.65 Å

= 50

I n c i d e n t B e a m

Intensity of scattered beam at 54 V







hypothesis, h=

2meV

de Broglie wavelength ofmoving electron at V = 54Volt is 1.67 Å which is inclose agreement with 1.65 Å.

12.27 Å=

Vor



0 5 10 15 20 25

Diffraction

pattern after

100 electrons

Diffractionpattern after

3000 electrons

Diffraction

pattern after

70000 electrons

Intensity vsThe Electron Microscope

Using wave-nature and particle nature ofelectronElectron is accelerated through a high voltageBetter than optical microscope

Shorter Wavelength : (up to 10-10 ) vs (10-7)Higher resolving power: nanometer vs. micro

24.3 Atomic structure

SF027 66

atom

Early models of atom

In 1898, Joseph John Thomson suggested a model of an atom

that consists of homogenous positively charged spheres with tiny

negatively charged electrons embedded throughout the sphere

as shown in the Figure.

The electrons much likes currants in a plum pudding.

atom.

positively

charged

sphere

electron

In 1911, Ernest Rutherford performed a critical

correct and proposed his new atomic model known

shown in Figure

nucleuselectron

pictured as electrons orbiting around a central

nucleus which concentrated of positive charge.

The electrons are accelerating because their

directions are constantly changing as they circle the

nucleus.

nucleuselectron



Based on the wave theory, an accelerating

charge emits energy.

Hence the electrons must emit the EM

radiation as they revolve around the nucleus.

+ Ze e

energy loss

As a result of the continuous loss of energy, the radii

of the electron orbits will be decreased steadily.

This would lead the electrons spiral and falls into the

nucleus, hence the atom would collapse as shown in

Figure.

+ Ze

e

energy loss

1. Only certain discrete orbits (stationary states) are

allowed for the electron

2. Electron in a stationary state does not radiate

3. Classical mechanics apply to electron in a stationary

state (not between states)

4. When an electron moves from one SS to another, a

change in energy occurs involving the emission (or

absorption) of a single photon of frequency v = E/h

5. Permitted orbits (SS) are those in which angular

momentum can take on only the discrete values

nh/2

force as the centripetal force he obtained

22

21

20

4 11

)4(4 nnh

mev e

+e

e

v

r

e F

In 1913, Neils Bohr proposed a

new atomic model based on

hydrogen atom.

assumes that each electron

moves in a circular orbit which is

centred on the nucleus, the

necessary centripetal force being

provided by the electrostatic force

of attraction between the

positively charged nucleus andthe negatively charged electron.

On this basis he was able to show that the energy ofan orbiting electron depends on the radius of its orbit.

This model has several features which are describedby the postulates (assumptions) stated below :

1. The electrons move only in certain circular orbits,called STATIONARY STATES or ENERGY LEVELS.When it is in one of these orbits, it does not radiateenergy.

2. The only permissible orbits are those in the discreteset for which the angular momentum of the electron L

equals an integer times h/ 2 . Mathematically,

2

nh L

2

nhmvr (11.1)

and m v r L

where

orbittheof radius:r electrontheof mass:m

,... , ,n 321numberquantum principal:

3. Emission or absorption of radiation occurs onlywhen an electron makes a transition from oneorbit to another .The frequency f of the emitted (absorbed) radiationis given by

if E E h f E

where

constantsPlanck':h

stateenergyfinal:f E

energyof change: E

stateenergyinitial:i E

If E f > E iIf E f < E i Emission of EM radiation

Absorption of EM radiation



Energy level of hydrogen atom

Consider one electron of charge e and mass m moves in a

circular orbit of radius r around a positively charged nucleus with

a velocity v.

The electrostatic force between electron and nucleus contributes

the centripetal force as write in the relation below:

ce F F centripetal force electrostatic force

r

m v

r

QQ 2

2

21

04

1and eQQ 21

r

emv

0

22

4(11.3)

+e

e v

r

e F

By taking square of both side of the equation, we get

By dividing the eqs. (11.4) and (11.3), thus

2

nhmvr

(11.4)2

22222

4

hnr vm

r

e

hn

mv

r vm

0

2

2

22

2

222

4

4

2

022

me

hnr and

k 4

10

electrostaticconstant

which r n is radii of the permissible orbits for the

where a0 is called the of hydrogenatom.

k m e

hnr

4

12

22

(11.5).. .3,2,1;4 22

22

nm ke

hnr n

02anr n

22

2

04 mke

ha

(11.6)

and

the radius of themost stable (lowest) orbit or ground state (n=1) inthe hydrogen atom and its value is

Unit conversion:

The radii of the orbits associated with allowed orbitsor states n are 4a0 ,9a0 , thus theradii are quantized.

2199312

234

0

1060.11000.91011.94

1063.6a

m1031.5 1 10a OR 0.531 Å (angstrom)

1 Å = 1.00 10 10 m

Energy level in hydrogen atom

is defined as a fixed energy corresponding to theorbits in which its electrons move around thenucleus.

The energy levels of atoms are quantized.

The total energy level E of the hydrogen atom isgiven by

K U E (11.7)

Kinetic energy of the electron Potential energy of the electron

Energy level in hydrogen atom

Potential energy U of the electron is given

by

r

QkQU 21 eQeQ 21 ;where

02 anr and

02

2

an

keU (11.8)

nucleus electron

Kinetic energy K of the electron is given by

Therefore the eq. (11.7) can be written as

2

2

1mv K

(11.9)

butr

emv

0

22

4

r

e K

0

2

42

1where k

04

1

02

2

2

1

an

ke K

02

2

02

2

2

1

an

ke

an

ke E n

and0

2 anr

20

21

2 na

ke E n (11.10)

In general, the total energy level E for the atom is

Using numerical value of k , e and a0, thus the eq. (11.10) can be

written as

2

2

0

2

2 n

Z

a

ke E n (11.11)

211

2199 1

1031.52

1060.11000.9

n E n

219

181

eV

1060.1

1017.2

n

1,2,3,...eV;6.13

2 n

n E n (11.12)

Note:

Eqs. (11.10) and (11.12) are valid for energy level of thehydrogen atom.

where n u m b e r a t o m ic: Z

where (orbi t)stateo f l eve lene rgy: t hn E n



The negative sign in the eq. (11.12) indicates that work has tobe done to remove the electron from the bound of the atom toinfinity, where it is considered to have zero energy.

The energy levels of the hydrogen atom are when

n=1, the ground state (the state of the lowest energy level) ;

n=2, the first excited state;

n=3, the second excited state;

n=4, the third excited state;

n= , the energy level is

eV613eV1

6.1321 . E

eV403eV2

6.1322 . E

0eV6.132

E

eV511eV3

6.13

23 . E

eV850eV4

6.1324 . E

electron is completelyremoved from the atom.

Figure 11.4 shows diagrammatically the various energy levels in thehydrogen atom.

excited state

is defined as helowest stableenergy state ofan atom.

is defined as he energy

levels that

higher thanhe ground

state.

(eV E nn

0.0

5 54.04 85.0

3 51.1

2 40.3

1 6.13

Excitation energyis defined as the energyrequired by an electron thatraises it to an excited statefrom its ground state.

Ionization energyis defined as theenergy requiredby an electron inthe ground stateto escapecompletely fromthe attraction ofthe nucleus.

An atom

becomes ion. Ground state

1st excited state

2nd excited state

3rd excited state4th excited state

Free electronFigure 11.4

Line spectrum

The emission lines correspond to the photonsof discrete energies that are emitted whenexcited atomic states in the gas make

transitions back to lower energy levels.

Line spectrum

Figure below shows line spectra produced by

emission in the visible range for hydrogen

(H), mercury (Hg) and neon (Ne).

Figure 11.5

Hydrogen Spectrum

= 656, 486, 434, 410 & 397 nm, what is the pattern?

Hydrogen emission line spectrum

Emission processes in hydrogen give rise to series,which are sequences of lines corresponding toatomic transitions.

The series in the hydrogen emission line spectrumare

Lyman series involves electron transitions that end at the ground state of hydrogen atom. It isin the ultraviolet (UV) range.

Balmer series involves electron transitions thatend at the 1st excited state of hydrogen atom. It

is in the visible light range.

Hydrogen emission line spectrum

The series in the hydrogen emission linespectrum are

Paschen series involves electron transitions that end at the 2nd excited state of hydrogen atom. Itis in the infrared (IR) range.

Brackett series involves electron transitions that

end at the 3rd excited state of hydrogen atom. It isin the IR range.

Pfund series involves electron transitions that endat the 4th excited state of hydrogen atom. It is inthe IR range.

Figure below shows diagrammatically the

series of hydrogen emission line spectrum.

)eV(n E 0.0

54.085.0

51.1

39.3

6.13

n

4

3

2

1

5

Ground state

1st excited state

2nd excited state

3rd excited state4th excited state

Free electron

Lyman series

Balmer series

Paschen series

Brackett seriesPfund series

Stimulation 11.1



in the Bohr model of a hydrogen atom.

Wavelength of hydrogen emission line

spectrum

If an electron makes a transition from an outer orbit oflevel ni to an inner orbit of level nf , thus the energy isradiated.The energy radiated in form of EM radiation(photon) where the wavelength is given by

hc E

hc

E 1

Wavelength of hydrogen emission line

spectrum

rd postulate, the eq. (11.13)

can be written as

hc E

hc

E 1

if

11nn E E

hcwhere

2

f 0

21

2f na

ke E n

and2

i0

21

2ina

ke E n

2

i0

2

2

f 0

21

2

1

2

11

na

ke

na

ke

hc

2i

2f 0

2 11

2

1

nna

ke

hc

2

i

2

f 0

211

2 nnhca

keand H R

hca

ke

0

2

2

2

i

2

f

111

nn R H

(11.14)

where17 m10097.1constantsRydberd': H R

nn of valuefinal:f

nn of valueinitial:i

Note: For the hydrogen line spectrum,

Lyman series( nf =1 )

Balmer series( nf =2 )

Paschen series( nf =3 )

Brackett series( nf =4 )

Pfund series( nf =5 )

To calculate the shortest wavelength in any series , take ni= .

2

i

2

1

1

11

n R H

2

i

2

1

2

11

n R H

2

i

2

1

3

11

n R H

2

i

2

1

4

11

n R H

2

i

2

1

5

11

n

R H

predicts successfully the energy levels of thehydrogen atom but fails to explain the energylevels of more complex atoms.

can explain the spectrum for hydrogen atom butsome details of the spectrum cannot be explainedespecially when the atom is placed in a magneticfield.

Magnetic field

Transitions

No magnetic field

1

2

Energy Levels

Spectra Figure 11.7

cannot explain the Zeeman effect

Zeeman effect is defined as the splittingof spectral lines when the radiatingatoms are placed in a magnetic field.

Magnetic field

Transitions

No magnetic field

1

2

Energy Levels

Spectra

24.4 X-ray



Review: Atoms

Smallest particle of matter that has theproperties of an element.

Contains a small, dense, positively chargedcenter (nucleus).

Nucleus surrounded by a negative cloud ofelectrons.

Electrons revolve in fixed, well-defined orbits(energy levels).

Review: Atoms

3 Fundamental Particles of an Atom

Electron

Proton

Neutron

Atoms

Electrons can only existin certain shells thatrepresent electronbinding energies

K, L, M shells (K isclosest to the nucleus)

The closer an electronis to the nucleus, thehigher the bindingenergy (strength ofattachment to thenucleus).

AtomsIn their normal state, atoms are electrically

neutral

If an atom has an extra electron or has had an

electron removed, it has been ionized.

How X-rays are CreatedTo produce x-rays, you need 3 things:

1. A source of electrons

2. A force to move them rapidly

3. Something to stop them rapidly

*All 3 conditions met in an x-ray tube

Early X-ray Tube Early X-ray Tube



The X-Ray tube is the single most important component of theradiographic system. It is the part that produces the X-rays

Wilhelm Conrad Röntgen (1845-1923)

A modern radiograph of a hand

History of X-ray and XRD

Wilhelm Conrad Röntgen discovered X-Rays in1895.1901 Nobel prize in Physics

Early use of X-Rays

Within few months of

their discovery, X-rays

were being put to

practical use.

This is an X-ray of bird

shot embedded in a

hand.

Unfortunately, much of

the early use of X-rays

was far too aggressive,

resulting in later cancer.

Section 9.4


Radiographs like theones in the last slide are

simply shadowgrams.The X-rays either passstraight through or arestopped by the object.The diagram on theupper left illustrates theprinciple and shows aperfect shadow.

History of X-ray and XRDIn reality, a large fractionof the X-rays are notsimply absorbed ortransmitted by the objectbut are scattered. Thediagram on the bottomleft illustrates this effectand illustrates the fuzzyedge of the object that is

produced in the image bythe scattered X-rays.

Max von Laue (1897-1960)

History of X-ray and XRDThe first kind of scatter process to berecognised was discovered by Maxvon Laue who was awarded the Nobelprize for physics in 1914 "for hisdiscovery of the diffraction of X-raysby crystals". His collaborators WalterFriedrich and Paul Knipping took thepicture on the bottom left in 1912. Itshows how a beam of X-rays isscattered into a characteristic pattern

by a crystal. In this case it is coppersulphate.

Max von Laue (1897-1960)


The X-ray diffraction pattern ofa pure substance is like afingerprint of the substance.The powder diffraction methodis thus ideally suited for

characterization andidentification of polycrystallinephases.

What are X-rays?

Beams of electromagnetic radiation

Short wavelength, high energy

Wave (sinusoidal, oscillating electric field with, at rightangles to it, a magnetic field)

wavelengthfrequency

Particle (photon)

Photon energy E E = h (h -34 Js)

Interacts

with

electrons!



Properties of a wave

Wave = c / (c=300.000 km/s)

Electromagnetic radiation

Å (Ångström) is non-SI unit of length X-rays: 10-8 to 10-11 m1 Å = 10-10 m = 0.1 to 100 Å

0.1 nm dimension of atoms, bonds, unit-

X-Rays

Electromagnetic radiation with short

wavelengths

Wavelengths less than for ultravioletWavelengths are typically about 0.1 nm

X-rays have the ability to penetrate most

materials with relative ease

High energy photons which can break

chemical bonds danger to tissue

Discovered and named by Roentgen in 1895

X-Rays

X-rays (discovered and named

by Roentgen): electromagnetic

radiation with short typicallyabout 0.1 nm wavelengths

X-rays have the ability to

penetrate most materials with

relative ease

X-rays are produced when

high-speed electrons are

suddenly slowed down

Wilhelm Conrad Röntgen

1845 1923

How are X-rays generated? A. Radioactive materials undergo decay (too many

nuclear particles or too high neutron/proton ratio)

1532P -> 16

32S + X-ray

How are X-rays generated? A. Machines

X-ray tube (accelerates electrons which

interact with electrons of target)

Particle accelerator

e-

X-ray tube

1. W filament isheated, electrons

2. Electrons are

accelerated inelectric field

3. Electrons interactwith target (anode), producing X-rays

TungstenFilament

Target (Co, Cu)

Electron beam

X-rays

Two types of X-radiation are produced:

Bremsstrahlung radiation), produces a continuous spectrum of X-ray wavelengths




2. Characteristic Radiation (X-rays of distinctwavelengths, unique for each element)

a) Incoming electronknocks inner shellelectron out of its

place b) Empty site is filled by

an electron from ahigher shell


2. Characteristic Radiation (X-rays of distinctwavelengths, unique for each element)

a) The difference in binding energy between inner andouter shell electrons

is released as X-rayof characteristicwavelength

Typical X-ray spectrum

Continuous radiation

= Bremsstrahlung

radiation

Characteristic radiation is

used in XRD, which

requires monochromatic

radiation

(eg. CuK = 1.5418 Å)

Production of X-rays

X-rays are produced

when high-speed

electrons are suddenly

slowed down

Can be caused by the

electron striking a

metal target

A current in the

filament causes

electrons to be emitted

Production of X-raysThese freed electrons

are accelerated toward

a dense metal target

The target is held at a

higher potential than the

filament

Production of X-rays (Bremsstrahlung) An electron passes near a

target nucleus and is

deflected from its path by its

attraction to the nucleus

This produces an acceleration

of the electron and hence

emission of electromagnetic

radiation

Production of X-rays (Bremsstrahlung)

If the electron loses all of its

energy in the collision, the

initial energy of the electron

is completely transformed

into a photon

The wavelength then is

max

min

hc e V h

min

hc

e V

Production of X-rays (Bremsstrahlung)

Not all radiation produced

is at this wavelength

Many electrons undergo

more than one collision

before being stopped

This results in the

continuous spectrum

produced



Characteristic X-Rays

When a metal target is

bombarded by high-energy

electrons, x-rays are

emitted

The x-ray spectrum

typically consists of a broad

continuous spectrum and a

series of sharp linesThe lines are dependent

on the metal of the target

The lines are called

characteristic x-rays

Characteristic X-Rays

The details of atomic structure can be used to explaincharacteristic x-rays

A bombarding electron collides with an electron in thetarget metal that is in an inner shell

If there is sufficient energy, the electron is removedfrom the target atom

The vacancy created by the lost electron is filled by anelectron falling to the vacancy from a higher energy

levelThe transition is accompanied by the emission of aphoton whose energy is equal to the differencebetween the two levels

X-ray Spectrum

The x-ray spectrum has

two distinct components

1) Bremsstrahlung: a

continuous broad

spectrum, which depends

on voltage applied to the

tube

2) The sharp, intense lines,

which depend on the

nature of the target material

Production of Characteristic Radiation

The X-ray Production X-rays are emitted when high energy electrons or any

other charged particles bombard a metal target.

The X-ray spectrum typically consists of a broad

continuous band containing a series of sharp lines.

The continuous spectrum is a result of collision

between incoming electrons and the target atoms.

The sharp lines are a result of the removal of inner

shell electrons of the target atoms.

Possible Interaction Between Electron Beam

and the Target

The X-ray Spectrum Some Features of the Spectrum

The energy of Bremsstrahlung radiation range from

zero to a maximum value which depends on the

potential difference applied on the tube.

The intensity of the low energy photons within the

spectrum is reduced because the absorption of the

target material.

The average energy of the X-ray beam is about one

third of the maximum.

The sharp lines, K,L,M etc stay at the same positions.

The line X-ray can be produced only when the

incoming electrons exceed some values.



31.2 X-ray diffraction

A modern Diffractometer

X-ray tube sample Detector

The X-ray diffractometer

Powder diffractometer with Bragg-Brentano geometry.

Analyst controls (choice of target in X-ray tube)

(positions of X-ray tube / sample / detector

n = 2 d sin

Experiment of Laue 1912

X-ray diffraction by a single crystal

What is X-ray diffraction?Scattering phenomenon, X-rays passing through

crystal

A tool for the characterisation of solid materials

based on their crystal structure

Used by

Earth Scientists

Chemists

Physicists

Material Scientists

Archaeologists

Rosalind E. Franklin 1952

What is XRD used for?Identification of minerals

Quantification of minerals

Determination of crystal structure

Unit-cell dimensions, symmetry, atom

Determination of grain sizes, strain

Typical samples

Minerals, rocks, corals, shells

What is X-ray diffraction?

XRD complements other analytical methods Visual

Need large crystals! cm

Optical microscopy (colour, birefringence,

µm to mm

SEM (composition: wt.% SiO2 What about polymorphs? (Calcite, Aragonite= CaCO3)

> 3 µm

XRF (composition: wt.% SiO2

What about polymorphs? (Calcite, Aragonite= CaCO3)

Interaction of X-rays with crystal structures

Crystal structure:

three-dimensional, periodic arrangement

of atoms in space.

Many different layers of atoms exist in a crystal

structure.

Each set of layers has a distinct interplanar distance

(d-spacing).

Unit-cell of NaCl

Cl Na



Interaction of X-rays with crystal structures

X-rays (electromagnetic wave) interact with the electrons

of the atoms in the crystal

Coherent Scatter : elastic collision between a photon (X-

ray) and and electron (in crystal)

- outgoing photons (X-ray) have same wavelength,

frequency and energy as incoming photons [XRD!]

Incoherent Scatter (= Compton scatter): inelastic collision

between photon and electron

- outgoing photons have lower energy

Interaction of X-rays with a scattering center

Every electron/atom in structure acts as a

scattering center, and is a source of spherical

waves of the same wavelength and frequency as

the incoming wave.

Incoming wave

+

+

-

-

Interference

Positive Negative

Interference Interference

Crests and troughs add up and

form a wave with twice the

amplitude.

Crests and troughs are offset

and cancel each other out.

This happens to most X-rays

scattered in crystals due to the

large number of scattering

centers ...

X-rays passing through a crystal lattice

X-rays

out of phase!

Diffraction

some X-rays to experience positive (or

constructive) interference in crystals. This is

called diffraction.

radiation coherently, the concerted

constructive interference at specific angles is

called diffraction

Diffraction in crystalline materials is best

described with= 2 dhkl sin

X-rays

in phase!

dhkl

For positive interference to occur, the path-difference must be equal to one wavelength ( or multiple wavelengths

(n .

n = 2 dhkl

sin

hkl

Diffraction of X-rays by Crystals

For diffraction to occur,the spacing between thegrooves must beapproximately equal tothe wavelength of theradiation to be measured

For X-rays, the regulararray of atoms in a crystalcan act as a three-dimensional grating fordiffracting X-rays

Schematic for X-ray Diffraction

A beam of X-rays with acontinuous range ofwavelengths is incident on thecrystal

The diffracted radiation is veryintense in certain directions

These directionscorrespond to constructive

interference from wavesreflected from the layers ofthe crystal

The diffraction pattern isdetected by photographic film



Photo of X-ray Diffraction Pattern

The array of spots is called a

Laue pattern

The crystal structure is

determined by analyzing the

positions and intensities of the

various spots

This is for NaCl

The beam reflected from thelower surface travels fartherthan the one reflected fromthe upper surface

If the path difference equalssome integral multiple of thewavelength, constructiveinterference occurs

gives theconditions for constructiveinterference

Constructive interference: 2dsin m

d 0.5nm in NaCl

For =.017nm

X-ray

d

1st maximum will be at 100

X-Ray Diffraction

Crystal solid such

as sodiumdsin

Bragg Equation

sin = (n )/2d

= angle of incidence

= wavelength

d = interplane distance of crystal

Bragg Equation

Incident angle

Reflected angle

Wavelength of X-ray

Total Diffracted

Angle

2

2

When the X-rays strike a layer of a crystal, some of

them will be reflected. We are interested in X-rays

that are in-phase with one another. X-rays that add

together constructively in x-ray diffraction analysis

in-phase before they are reflected and after they

reflected.

The line CE isequivalent

to the distancebetween the twolayers (d)

Bragg EquationThese two x-ray beams travel slightly different

distances. The difference in the distances traveled is

related to the distance between the adjacent layers.

Connecting the two beams with perpendicular lines

shows the difference between the top and the

bottom beams.

sin E d

sin EF d

The length DE is the same as EF, so the totaldistance traveled by the bottom wave is expressedby:

Constructive interference of the radiation fromsuccessive planes occurs when the path differenceis an integral number of wavelenghts. This is theBragg Law.

sin DE d

2 sin DE EF d

2 sinn d

Bragg Equation

nd sin2

where, d is the spacing of the planes and n is theorder of diffraction.

Bragg reflection can only occur for wavelength

This is why we cannot use visible light. No diffractionoccurs when the above condition is not satisfied .

The diffracted beams (reflections) from any set oflattice planes can only occur at particular anglespradicted by the Bragg law.

d n 2



Arthur Holly Compton

1892 1962

Discovered the Comptoneffect

Worked with cosmic rays

Director of the lab at U ofChicago

Shared Nobel Prize in 1927

The Compton Effect

Compton directed a beam of x-rays toward a block ofgraphite

He found that the scattered x-rays had a slightlylonger wavelength that the incident x-rays

This means they also had less energy

The amount of energy reduction depended on theangle at which the x-rays were scattered

The change in wavelength is called the Compton shift

Compton Scattering

Compton assumed the photons acted like otherparticles in collisions

Energy and momentum were conserved

The shift in wavelength is

(1 cos )o

e

h

m c

Compton Scattering

The quantity h/mec is called the Compton wavelength

Compton wavelength = 0.002 43 nm

Very small compared to visible light

The Compton shift depends on the scattering angleand not on the wavelength

Experiments confirm the results of Comptonscattering and strongly support the photon concept

Three-Dimensional Conformal Radiation

Therapy (3D-CRT)

Tumors usually have an irregularshape

Three-dimensional conformalradiation therapy (3D-CRT) usessophisticated computers and CTscans and/or MRI scans to createdetailed 3-D representations ofthe tumor and surroundingorgans

Three-Dimensional Conformal Radiation

Therapy (3D-CRT)

Radiation beams are thenshaped exactly to the size andshape of the tumor

Because the radiation beams are very precisely directed, nearbynormal tissue receives lessradiation exposure

Sample

We are choosing incoming angle =

outgoing angle.

Therefore only diffraction from

atomic planes in the crystal

structure that are parallel to the flat

sample surface are detected

For example, if we analysed this

single muscovite crystal with XRD,

lying flat on the sample holder with

its 001 plane, only (001) planes

would diffract.

muscovite

(001)

sample

Powder X-ray Diffraction

Sample

However, we want ALL

crystallographic planes to

contribute to the XRD pattern.

All samples need to be ground

up very finely (ideally 1-10 µm

grain size), and the grainsoriented randomly in the

sample holder.muscovite

(001)

sample

Powder X-ray Diffraction



24.5 Nanoscience

Nanoscience refers to the ability to manipulateindividual atoms and molecules, making itpossible to build machines on the scale ofhuman cells.

Nanotechnology

Nanotechnology is the understanding andcontrol of matter at dimensions of roughly 1 to100 nanometers.Nanotechnology involves imaging, measuring,modeling, and manipulating matter at thislength scale.

Nanoscale

At the nanoscale, the physical, chemical, andbiological properties of materials differ infundamental and valuable ways from the

properties of individual atoms and molecules orbulk matter.Nanotechnology R&D is directed towardunderstanding and creating improvedmaterials, devices, and systems that exploitthese new properties

Facts

A nanometer is one billionth of a meter.In 2005 the US government spent an estimated$1,081 million

While difficult to measure accurately, somehave estimated that worldwide governmentfunding has increased to about five times whatit was in 1997, exceeding $2 billion in 2002.

CMOS TECHNOLOGY

Introduction178

(released March 2004):

150 million transistors

90 nm design rules

3.4 GHz clock frequency

DRAM chips:

4 Gb chips demonstrated

(~ 109 transistors/cm2)

- 130 nm) processor

Now chips based on thedesign rules of 22 nm are onthe way.

In 2004 we were already inside nanotechnology!

One area of nanotechnology R&D is medicine.Medical researchers work at the micro- andnano-scales to develop new drug deliverymethods, therapeutics and pharmaceuticals.For a bit of perspective, the diameter of DNA,our genetic material, is in the 2.5 nanometer

range, while red blood cells are approximately2.5 micrometers.

Applications/Products

-

limited), nanoparticles are being used in anumber of industries. Nanoscale materials areused in electronic, magnetic andoptoelectronic, biomedical, pharmaceutical,

cosmetic, energy, catalytic and materialsapplications. Areas producing the greatestrevenue for nanoparticles reportedly arechemical-mechanical polishing, magneticrecording tapes, sunscreens, automotivecatalyst supports, biolabeling,

Nanotechnology has thepotential to profoundlychange our economy and toimprove our standard ofliving, in a manner not unlikethe impact made by advances

over the past two decades byinformation technology. It isquite possibly the next step intechnology that will lead togreat innovations. If thecapabilities of nanoscience arefully harnessed, anythingcould be possible.



Numerous products featuring the uniqueproperties of nanoscale materials are availableto consumers and industry today. Mostcomputer hard drives, for instance, containgiant magnetoresistance (GMR) heads that,through nano-thin layers of magneticmaterials, allow for a significant increase in

storage capacity. Other electronic applicationsinclude non-volatile magnetic memory,automotive sensors, landmine detectors andsolid-state compasses

Nanomaterials

Examples are nanoscale particles, tubes androds.

Nanotube

Nanoparticles

Nanorods

Some other uses

Burn and wounddressings Water filtration

Catalysis A dental-bondingagentStep assists on vans.Coatings for easiercleaning glassBumpers andcatalytic converterson cars

Protective and glare-reducing coatings foreyeglasses and cars

Sunscreens andcosmetics.Longer-lasting tennisballs.Light-weight,stronger tennisracquets.Stain-free clothingand mattresses.Ink.

Medical uses

The pharmaceutical and chemical industries arebeing impacted greatly by nanotechnology, as well. New commercial applications ofnanotechnology that are expected in two to five years in these industries include:advanced drug delivery systems, includingimplantable devices that automaticallyadminister drugs and sensor drug levels andmedical diagnostic tools, such as cancer taggingmechanisms.

Bibliographyhttp://www.nsf.gov/news/overviews/nano/index.jsp http://www.nanoscience.com/education/index.html http://www.nsf.gov/discoveries/index.jsp?prio_area=10

chapter24 quantum physics

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