Outline 24. QUANTUM PHYSICS Liew Sau Poh …chunghuastpm.weebly.com/.../chapter24_0quantum_physics.pdf24. QUANTUM PHYSICS Liew Sau Poh Outline 24.1 Photons 24.2 Wave-particle duality

24. QUANTUM PHYSICS

Liew Sau Poh

Outline 24.1 Photons 24.2 Wave-particle duality 24.3 Atomic structure 24.4 X-rays 24.5 Nanoscience

Objectives (a) describe important observations in

photoelectric emission experiments (b) recognise features of photoelectric emission

that cannot be explained by wave theory and explain these features using the concept of quantisation of light

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

threshold frequency

Objectives (e

effect, hf=W + ½mv2max

(f) understand the meaning of stopping potential and use eVs= ½mv2

max

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

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

Objectives (j) explain the advantages of an electron

microscope as compared to an optical microscope

(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 transitions between energy levels

(o) explain the concepts of excitation energy and ionisation energy

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

(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 parallel

adjacent 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 to

the surface of a metal, electrons are ejected from the surface.

Photoelectrons: The electrons emitted by this effect. UV

Metals Metals other than Alkali Metals Alkali Metals

Visible light

No photoelectrons Photoelectrons Photoelectrons

Visible light

Photon A packet or bundle of energy is called a photon. 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

c E c2 =

p = h

E 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 exist at 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 the photon; so the energy of the photon does not change when photon travels from one medium to another.

Properties of photons Wavelength of the photon changes in different media; so, velocity of a photon is different in different media. Photons are electrically neutral. Photons may show diffraction under given conditions. Photons are not deviated by magnetic and electric fields.

Metals other than Alkali Metals

Visible light No photoelectrons

UV

Metals

Photoelectrons

Alkali Metals

Photoelectrons Visible light

Photoelectric Effect

Photoelectric Effect The phenomenon of emission of electrons from mainly metal surfaces exposed to light energy (X rays, rays, UV rays, Visible light and even Infra Red rays) of suitable frequency is known as photoelectric effect. The electrons emitted by this effect are called photoelectrons. The current constituted by photoelectrons is known as photoelectric current. Note: Non metals also show photoelectric effect. Liquids and gases also show this effect but to limited extent.

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 lights but not UV light. Quartz transmits UV light. When light of suitable frequency falls on the metallic cathode, photoelectrons are emitted. These photoelectrons are attracted towards the +ve anode and hence photoelectric current is constituted.

I A

Intensity (L) 0


1) Effect of Intensity of Incident Light on Photoelectric Current: For a fixed frequency, the photoelectric current increases linearly with increase in intensity of incident light.

0

Saturation Current

L1

L2

L2 > L1

I A

+ Potential of A (V) VS

Experimental (Photoelectric Effect) 2) Effect of Potential on

Photoelectric Current: For a fixed frequency and intensity of incident light, the photoelectric current increases with increase in +ve potential applied to the anode. When all the photoelectrons reach the plate A, current becomes maximum and is known as saturation current.

0

Saturation Current

L1

L2

L2 > L1

I A



Photoelectric Current: When the potential is decreased, the current decreases but does not become zero at zero potential. This shows that even in the absence of accelerating potential, a few photoelectrons manage to reach the plate on their own due to their K.E.

0

Saturation Current

L1

L2

L2 > L1

I A



Photoelectric Current: When ve potential is applied to the plate A w.r.t. C, photoelectric current becomes zero at a particular value of ve potential called stopping potential or cut-off potential. Intensity of incident light does not affect the stopping potential.

I A

Potential of A (V) 0 VS1 +

Saturation Current

1

2

2 > 1

VS2

Experimental (Photoelectric Effect) 3) Effect of Frequency of Incident

Light on Photoelectric Current: For a fixed intensity of incident light, the photoelectric current does not depend on the frequency of the incident light. Because, the photoelectric current simply depends on the number of photoelectrons emitted and in turn on the number of photons incident and not on the energy of photons.

I A


Saturation Current

1

2

2 > 1

VS2

Experimental (Photoelectric Effect) 4) Effect of Frequency of

Incident Light on Stopping Potential: For a fixed intensity of incident light, the photoelectric current increases and is saturated with increase in +ve potential applied to the anode. However, the saturation current is same for different frequencies of the incident lights.

I A


Saturation Current

1

2

2 > 1

VS2

Experimental (Photoelectric Effect) 4) Effect of Frequency of

Incident Light on Stopping Potential: When potential is decreased and taken below zero, photoelectric current decreases to zero but at different stopping potentials for different frequencies.

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

VS (V)

0 0

5) Threshold Frequency The graph between stopping potential and frequency does not pass through the origin. It shows that there is a minimum value of frequency called threshold frequency below which photoelectric emission is not possible however high the intensity of incident light may be. It depends on the nature of the metal emitting 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 called threshold frequency below which no photoelectric emission is possible, howsoever, the intensity of incident light may be. The number of photoelectrons emitted per second (i.e. photoelectric current) is directly proportional to the intensity of incident light provided the frequency is above the threshold frequency.

Laws of Photoelectric Emission The maximum kinetic energy of the photoelectrons is directly proportional to the frequency provided the frequency is above the threshold frequency. The maximum kinetic energy of the photoelectrons is independent of the intensity of the incident light. The process of photoelectric emission is instantaneous. i.e. as soon as the photon of suitable frequency falls on the substance, it emits photoelectrons. The photoelectric emission is one-to-one. i.e. for every photon of suitable frequency one electron is emitted.

the energy of the photon is absorbed by the electron and is used in two ways: A part of energy is used to overcome the surface barrier 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 mv2

max

According to law of conservation of energy, hf = + ½ mv2

max = hf0 + ½ mv2

max ½ mv2

max = h ( f - f0 )

Photon h

Metal

Photoelectron

½ mv2max

= h 0

½ mv2max = h ( - 0 )

Verification of Laws of Photoelectric Emission based

If < 0, then ½ mv2max is negative, which is

not possible. Therefore, for photoelectric emission to take place > 0. Since one photon emits one electron, so the number photoelectrons emitted per second is directly proportional to the intensity of incident light.

½ mv2max = h ( - 0 )

Verification of Laws of Photoelectric Emission based

It is clear that ½ mv2max as h and 0 are constant.

This shows that K.E. of the photoelectrons is directly proportional to the frequency of the incident light. Photoelectric emission is due to collision between a photon and an electron. As such there can not be any significant time lag between the incidence of photon and 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 Television transmission Reproduction of sound in cinema film In paper industry to measure the thickness of paper To locate flaws or holes in the finished goods In astronomy To determine opacity of solids and liquids

Automatic switching of street lights To control the temperature of furnace Photometry Beauty meter To measure the fair complexion of skin Light meters used in cinema industry to check the light Photoelectric sorting Photo counting Meteorology

Photoelectric Threshold Binding Energies

K: 100 L: 50 M: 20

Photon in

Photon energy: 15

Which shells are candidates for photoelectric interactions?

Photoelectric Threshold

Photon in

Photon energy: 15

NO

NO

NO

Binding Energies K: 100 L: 50 M: 20



Photon in

Photon energy: 25 Binding Energies

K: 100 L: 50 M: 20



Photon in

Photon energy: 25

NO

NO

YES




Photon in

Photon energy: 22

Which photon has a greater probability for photoelectric interactions with the m shell?

Photon energy: 25

A

B

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



Photon in

Photon energy: 55




Photon in

Photon energy: 55


NO

YES

YES



Photon in

Photon energy: 105 Binding Energies

K: 100 L: 50 M: 20



Photon energy: 105

YES

YES

YES




Photoelectric interactions decrease with increasing photon energy

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


Binding Energies K: 50 L: 25

Photon energy: 49

NO

YES

Photon energy: 51

YES

YES

When photon energy just reaches binding energy of next (inner) shell, photoelectric interaction now possible with that shell

shell offers new candidate target electrons

Photoelectric Threshold 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

Interaction Probability

K-shell interactions possible

L-shell interactions

possible L-shell binding energy

K-shell binding energy

M-shell interactions

possible

Photoelectric Threshold causes step increases in interaction probability as photon energy exceeds shell binding energies

Photon Energy

Interaction Probability L-edge

K-edge

24.2 Wave-particle Duality

Dual Nature of Radiation and Matter

Wave theory of electromagnetic radiations explained the phenomenon of interference, diffraction and polarization. On the other hand, quantum theory of e.m. radiations successfully explained the photoelectric effect, Compton effect, black body radiations, X- ray spectra, etc. Thus, radiations have dual nature. i.e. wave and particle nature.

Dual Nature of Radiation and Matter Louis de Broglie suggested that the particles like electrons, 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 a particle and as a wave simultaneously. It is either the one 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 and both entities must be symmetrical.

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

Expression for de Broglie wave According to quantum theory, the energy of the photon is

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

E = h = hc

E = mc2

So = h mc

or = h p

where p = mc is momentum of a photon

= h mv

The Compton Effect Let the light is made up of particles (photons), and that photons have momentum, with energy hf collides with a stationary electron. Some of the energy and momentum is transferred to the electron (this is known as the Compton effect), but both energy and momentum are conserved (elastic collision). After the collision the photon has energy hf and the electron has acquired a kinetic energy K. Conservation of energy: hf = hf + K

Conclusion de 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 wavelength is infinite. Such a wave can not be visualized. de Broglie wavelength is inversely proportional to the mass of the particle. The wavelength associated with a heavier particle is smaller than that with a lighter particle. de Broglie wavelength is independent of the charge of the particle.

= h mv

Conclusion Matter waves, similar to electromagnetic waves, can travel in vacuum and hence they are not mechanical waves. Matter waves are not electromagnetic waves because they are not produced by accelerated charges. Matter waves are probability waves, amplitude of which gives the probability of existence of the particle at the point.

= h mv

Davisson and Germer Experiment A beam of electrons emitted by the electron gun is made to fall on Nickel crystal cut along cubical axis at a particular angle. The scattered beam of electrons is received by the detector which can be rotated at any angle.

F

V

C A

Nickel Crystal

Electron Gun

Crystal Lattice

Davisson and Germer Experiment The energy of the incident beam of electrons can be varied by changing the applied voltage to the electron gun. Intensity of scattered beam of electrons is found to be maximum when angle of scattering is 50° and the accelerating potential is 54 V.

F

V

C A

Nickel Crystal

Electron Gun

Crystal Lattice

Davisson and Germer Experiment + 50° + = 180°

i.e. = 65°

For Ni crystal, lattice spacing d = 0.91 Å

For first principal maximum, n = 1

Electron diffraction is similar to X-ray diffraction.

F

V

C A

Nickel Crystal

Electron Gun

Crystal Lattice

2dsin = n gives = 1.65 Å

= 50

Inci

dent

Bea

m

Intensity of scattered beam at 54 V

Inci

dent

Bea

m


Inci

dent

Bea

m


Inci

dent

Bea

m


hypothesis, h = 2meV

de Broglie wavelength of moving electron at V = 54 Volt is 1.67 Å which is in close agreement with 1.65 Å.

12.27 Å = V

or

0 5 10 15 20 25

Diffraction pattern after 100 electrons



Intensity vs The Electron Microscope Using wave-nature and particle nature of electron Electron is accelerated through a high voltage Better 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

nucleus electron

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.

nucleus electron

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

reF

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 and the negatively charged electron.

On this basis he was able to show that the energy of an orbiting electron depends on the radius of its orbit. This model has several features which are described by 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 radiate energy.

2. The only permissible orbits are those in the discrete set for which the angular momentum of the electron L equals an integer times h/2 . Mathematically,

2nhL

2nhmvr (11.1)

and m vrL

where

orbit theof radius: relectron theof mass:m

,...,,n 321number quantum principal:

3. Emission or absorption of radiation occurs only

when an electron makes a transition from one orbit to another.

The frequency f of the emitted (absorbed) radiation is given by if EEhfE

where constant sPlanck': h

stateenergy final:fE

energy of change: E

stateenergy initial:iE

If Ef > Ei

If Ef < Ei 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 FF centripetal force electrostatic force

rmv

rQQ 2

221

041

and eQQ 21

remv

0

22

4(11.3)

+e

e v

reF

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

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

2nhmvr

(11.4) 2

22222

4hnrvm

re

hn

mvrvm

0

2

2

22

2

222

4

4

20

22

mehnr and

k41

0

electrostatic constant

which rn is radii of the permissible orbits for the

where a0 is called the of hydrogen atom.

kmehnr

41

2

22

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

22 n

mkehnrn

02 anrn

22

2

0 4 mkeha

(11.6)

and

the radius of the most stable (lowest) orbit or ground state (n=1) in the hydrogen atom and its value is Unit conversion:

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

2199312

234

01060.11000.91011.94

1063.6a

m 1031.5 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 the orbits in which its electrons move around the nucleus. The energy levels of atoms are quantized. The total energy level E of the hydrogen atom is given by

KUE (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

rQkQU 21 eQeQ 21 ;where

02 anrand

02

2

ankeU (11.8)

nucleus electron

Kinetic energy K of the electron is given by Therefore the eq. (11.7) can be written as

2

21 mvK

(11.9)

but r

emv0

22

4

reK

0

2

421

where k04

1

02

2

21

ankeK

02

2

02

2

21

anke

ankeE n

and 02 anr

20

2 12 nakeEn (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 nZ

akeEn (11.11)

211

2199 11031.52

1060.11000.9n

E n

219

18 1eV1060.11017.2

n

1,2,3,... eV; 6.132 n

nEn (11.12)

Note:

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

where n u m b e r a to m ic :Z

where (o r b it) s ta te o f le v e le n e r gy : t hnE n

The negative sign in the eq. (11.12) indicates that work has to be done to remove the electron from the bound of the atom to infinity, 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

eV 613eV 1

6.1321 .E

eV 403eV 2

6.1322 .E

0eV 6.132E

eV 511eV 3

6.1323 .E

eV 850eV 4

6.1324 .E

electron is completely removed from the atom.

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

excited state

is defined as the lowest stable energy state of an atom.

is defined as the energy levels that higher than the ground state.

)(eVE nn0.0

5 5 4.04 8 5.03 51.1

2 4 0.3

1 6.13

Excitation energy is defined as the energy required by an electron that raises it to an excited state from its ground state.

Ionization energy is defined as the energy required by an electron in the ground state to escape completely from the attraction of the nucleus.

An atom becomes ion. Ground state

1st excited state

2nd excited state 3rd excited state 4th excited state

Free electron Figure 11.4

Line spectrum The emission lines correspond to the photons of discrete energies that are emitted when excited 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 to atomic transitions. The series in the hydrogen emission line spectrum are

Lyman series involves electron transitions that end at the ground state of hydrogen atom. It is in the ultraviolet (UV) range. Balmer series involves electron transitions that end 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 line spectrum are

Paschen series involves electron transitions that end at the 2nd excited state of hydrogen atom. It is in the infrared (IR) range. Brackett series involves electron transitions that end at the 3rd excited state of hydrogen atom. It is in the IR range. Pfund series involves electron transitions that end at the 4th excited state of hydrogen atom. It is in the IR range.

Figure below shows diagrammatically the series of hydrogen emission line spectrum.

)eV(nE0.0

5 4.08 5.051.1

3 9.3

6.13

n

43

2

1

5

Ground state

1st excited state

2nd excited state 3rd excited state 4th excited state

Free electron

Lyman series

Balmer series

Paschen series Brackett series

Pfund 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 of level ni to an inner orbit of level nf, thus the energy is radiated. The energy radiated in form of EM radiation (photon) where the wavelength is given by

hcEhcE1

Wavelength of hydrogen emission line spectrum

rd postulate, the eq. (11.13) can be written as

hcEhcE1

if

11nn EE

hcwhere 2

f0

2 12f nakeEn

and 2

i0

2 12i nakeEn

2i0

2

2f0

2 12

12

11na

kena

kehc

2i

2f0

2 112

1nna

kehc

2i

2f0

2 112 nnhca

keand HR

hcake

0

2

2

2i

2f

111nn

RH (11.14)

where 17 m 10097.1constant sRydberd': HR 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= .

2i

21

111

nRH

2i

21

211

nRH

2i

21

311

nRH

2i

21

411

nRH

2i

21

511

nRH

predicts successfully the energy levels of the hydrogen atom but fails to explain the energy levels of more complex atoms. can explain the spectrum for hydrogen atom but some details of the spectrum cannot be explained especially when the atom is placed in a magnetic field.

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 splitting of spectral lines when the radiating atoms 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 the properties of an element. Contains a small, dense, positively charged center (nucleus). Nucleus surrounded by a negative cloud of electrons. Electrons revolve in fixed, well-defined orbits (energy levels).

Review: Atoms

3 Fundamental Particles of an Atom Electron Proton Neutron

Atoms Electrons can only exist in certain shells that represent electron binding energies K, L, M shells (K is closest to the nucleus) The closer an electron is to the nucleus, the higher the binding energy (strength of attachment to the nucleus).

Atoms In 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 Created To 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 the radiographic 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 in 1895. 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

History of X-ray and XRD Radiographs like the ones in the last slide are simply shadowgrams. The X-rays either pass straight through or are stopped by the object. The diagram on the upper left illustrates the principle and shows a perfect shadow.

History of X-ray and XRD In reality, a large fraction of the X-rays are not simply absorbed or transmitted by the object but are scattered. The diagram on the bottom left illustrates this effect and illustrates the fuzzy edge of the object that is produced in the image by the scattered X-rays.

Max von Laue (1897-1960)

History of X-ray and XRD The first kind of scatter process to be recognised was discovered by Max von Laue who was awarded the Nobel prize for physics in 1914 "for his discovery of the diffraction of X-rays by crystals". His collaborators Walter Friedrich and Paul Knipping took the picture on the bottom left in 1912. It shows how a beam of X-rays is scattered into a characteristic pattern by a crystal. In this case it is copper sulphate.

Max von Laue (1897-1960)

History of X-ray and XRD The X-ray diffraction pattern of a pure substance is like a fingerprint of the substance. The powder diffraction method is thus ideally suited for characterization and identification of polycrystalline phases.

What are X-rays? Beams of electromagnetic radiation

Short wavelength, high energy

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

wavelength frequency

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 m 1 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 ultraviolet Wavelengths 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 typically about 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 is heated, electrons

2. Electrons are accelerated in electric field

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

Tungsten Filament

Target (Co, Cu)

Electron beam

X-rays

Two types of X-radiation are produced: Bremsstrahlung radiation), produces a continuous spectrum of X-ray wavelengths

Two types of X-radiation are produced: 2. Characteristic Radiation (X-rays of distinct wavelengths, unique for each element)

a) Incoming electron

knocks inner shell electron out of its place

b) Empty site is filled by an electron from a higher shell

Two types of X-radiation are produced: 2. Characteristic Radiation (X-rays of distinct wavelengths, unique for each element)

a) The difference in binding energy between inner and outer shell electrons is released as X-ray of characteristic wavelength

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-rays These 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

maxmin

hce V h

minhc

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 lines

The 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 explain characteristic x-rays

A bombarding electron collides with an electron in the target metal that is in an inner shell If there is sufficient energy, the electron is removed from the target atom The vacancy created by the lost electron is filled by an electron falling to the vacancy from a higher energy level The transition is accompanied by the emission of a photon whose energy is equal to the difference between 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 the grooves must be approximately equal to the wavelength of the radiation to be measured For X-rays, the regular array of atoms in a crystal can act as a three-dimensional grating for diffracting X-rays

Schematic for X-ray Diffraction A beam of X-rays with a continuous range of wavelengths is incident on the crystal The diffracted radiation is very intense in certain directions

These directions correspond to constructive interference from waves reflected from the layers of the crystal

The diffraction pattern is detected 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 the lower surface travels farther than the one reflected from the upper surface If the path difference equals some integral multiple of the wavelength, constructive interference occurs

gives the conditions for constructive interference

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 sodium dsin

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 is equivalent to the distance between the two layers (d)

Bragg Equation These 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.

sinDE d

sinEF d

The length DE is the same as EF, so the total distance traveled by the bottom wave is expressed by: Constructive interference of the radiation from successive planes occurs when the path difference is an integral number of wavelenghts. This is the Bragg Law.

sinDE d2 sinDE EF d

2 sinn d

Bragg Equation

nd sin2

where, d is the spacing of the planes and n is the order of diffraction. Bragg reflection can only occur for wavelength This is why we cannot use visible light. No diffraction occurs when the above condition is not satisfied. The diffracted beams (reflections) from any set of lattice planes can only occur at particular angles pradicted by the Bragg law.

dn 2

Arthur Holly Compton 1892 1962 Discovered the Compton effect Worked with cosmic rays Director of the lab at U of Chicago Shared Nobel Prize in 1927

The Compton Effect Compton directed a beam of x-rays toward a block of graphite He found that the scattered x-rays had a slightly longer wavelength that the incident x-rays

This means they also had less energy The amount of energy reduction depended on the angle at which the x-rays were scattered The change in wavelength is called the Compton shift

Compton Scattering Compton assumed the photons acted like other particles in collisions Energy and momentum were conserved The shift in wavelength is

(1 cos )o

e

hm 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 angle and not on the wavelength Experiments confirm the results of Compton scattering and strongly support the photon concept

Three-Dimensional Conformal Radiation Therapy (3D-CRT)

Tumors usually have an irregular shape Three-dimensional conformal radiation therapy (3D-CRT) uses sophisticated computers and CT scans and/or MRI scans to create detailed 3-D representations of the tumor and surrounding organs

Three-Dimensional Conformal Radiation Therapy (3D-CRT)

Radiation beams are then shaped exactly to the size and shape of the tumor Because the radiation beams are very precisely directed, nearby normal tissue receives less radiation 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 grains oriented randomly in the sample holder.

muscovite

(001)

sample

Powder X-ray Diffraction

24.5 Nanoscience Nanoscience refers to the ability to manipulate individual atoms and molecules, making it possible to build machines on the scale of human cells.

Nanotechnology Nanotechnology is the understanding and control of matter at dimensions of roughly 1 to 100 nanometers. Nanotechnology involves imaging, measuring, modeling, and manipulating matter at this length scale.

Nanoscale At the nanoscale, the physical, chemical, and biological properties of materials differ in fundamental and valuable ways from the properties of individual atoms and molecules or bulk matter. Nanotechnology R&D is directed toward understanding and creating improved materials, devices, and systems that exploit these 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, some have estimated that worldwide government funding has increased to about five times what it was in 1997, exceeding $2 billion in 2002.

CMOS TECHNOLOGY

Introduction 178

(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 the design rules of 22 nm are on the way.

In 2004 we were already inside nanotechnology!

One area of nanotechnology R&D is medicine. Medical researchers work at the micro- and nano-scales to develop new drug delivery methods, 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 approximately 2.5 micrometers.

Applications/Products -

limited), nanoparticles are being used in a number of industries. Nanoscale materials are used in electronic, magnetic and optoelectronic, biomedical, pharmaceutical, cosmetic, energy, catalytic and materials applications. Areas producing the greatest revenue for nanoparticles reportedly are chemical-mechanical polishing, magnetic recording tapes, sunscreens, automotive catalyst supports, biolabeling,

Nanotechnology has the potential to profoundly change our economy and to improve our standard of living, in a manner not unlike the impact made by advances over the past two decades by information technology. It is quite possibly the next step in technology that will lead to great innovations. If the capabilities of nanoscience are fully harnessed, anything could be possible.

Numerous products featuring the unique properties of nanoscale materials are available to consumers and industry today. Most computer hard drives, for instance, contain giant magnetoresistance (GMR) heads that, through nano-thin layers of magnetic materials, allow for a significant increase in storage capacity. Other electronic applications include non-volatile magnetic memory, automotive sensors, landmine detectors and solid-state compasses

Nanomaterials Examples are nanoscale particles, tubes and rods.

Nanotube

Nanoparticles

Nanorods

Some other uses Burn and wound dressings Water filtration Catalysis A dental-bonding agent Step assists on vans. Coatings for easier cleaning glass Bumpers and catalytic converters on cars

Protective and glare-reducing coatings for eyeglasses and cars Sunscreens and cosmetics. Longer-lasting tennis balls. Light-weight, stronger tennis racquets. Stain-free clothing and mattresses. Ink.

Medical uses

The pharmaceutical and chemical industries are being impacted greatly by nanotechnology, as well. New commercial applications of nanotechnology that are expected in two to five years in these industries include: advanced drug delivery systems, including implantable devices that automatically administer drugs and sensor drug levels and medical diagnostic tools, such as cancer tagging mechanisms.

Bibliography http://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

Documents

Outline 24. QUANTUM PHYSICS Liew Sau Poh …chunghuastpm.weebly.com/.../chapter24_0quantum_physics.pdf24. QUANTUM PHYSICS Liew Sau Poh Outline 24.1 Photons 24.2 Wave-particle duality