4. Compton Effect-ok

7/29/2019 4. Compton Effect-ok

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Compton scattering 1

Expectation from classicalelectrodynamics:

radiation incident onfree electrons electrons oscillate atfrequency of incidentradiation emit lightof same frequency light scattered in alldirections

electrons dont gainenergy

no change in frequencyof light

Scattering of X-rays on free

electrons; Electrons supplied by graphitetarget; Outermost electrons in C looselybound; binding energy


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Compton (1923) measured intensity of

scattered X-rays from solid target, asfunction of wavelength for differentangles. Nobel prize 1927.

X-ray source

Target

Crystal(selectswavelength)

Collimator(selects angle)

Result: peak in scattered radiation shifts to longerwavelength than source. Amount depends on (but

not on the target material).A.H. Compton,Phys. Rev. 22 409 (1923)


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Classical picture: oscillating electromagnetic field causesoscillations in positions of charged particles, which re-radiate inall directions at same frequencyas incident radiation. No changein wavelength of scattered light is expected

Comptons explanation: collisions between particles of light (X-ray photons) and electrons in the material

Oscillating electronIncident light wave Emitted light wave

ep

pBefore After

Electron

Incoming photon

p

scattered photon

scattered electron


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ep

pBefore After

Electron

Incoming photon

p

scattered photon

scattered electron

Conservation of energy Conservation of momentum

1/ 2

2 2 2 2 4

e e eh m c h p c m c

e

h

p i p p

1 cos

1 cos 0

e

c

h

m c

12Compton wavelength 2.4 10 mce

hm c

From this derive change in wavelength:


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unshifted peaks come fromcollision between the X-rayphoton and the nucleus of theatom

- = (h/mNc)(1 - cos) 0since mN >> me


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WAVE-PARTICLE DUALITY OF LIGHT

Einstein (1924) : There are therefore now two theories oflight, both indispensable, and without any logical connection.

evidence for wave-nature of light:

diffraction

interference

evidence for particle-nature of light: photoelectric effect

Compton effect

Light exhibits diffraction and interference phenomena thatare onlyexplicable in terms of wave properties

Light is always detected as packets (photons); we never observehalf a photon

Number of photons proportional to energy density (i.e. tosquare of electromagnetic field strength)


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Double slit experimentOriginally performed by Young (1801) to demonstrate the wave-nature of

light. Has now been done with electrons, neutrons, He atoms,

D

d

Detectingscreen

y

Alternativemethod ofdetection: scan adetector acrossthe plane andrecord number ofarrivals at eachpoint

Expectation: two peaks for particles, interference pattern for waves


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Maxima when:

sind n

y D

Dy

d

Position on screen: tany D D

n

d

d

D >> d use small angle approximation

So separation between adjacent maxima:

Fringe spacing in double slit experiment

d

sind

D

y


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Double slit experiment -- interpretation

classical:

two slits are coherent sources of light interference due to superposition of secondary waves on

screen intensity minima and maxima governed by optical path

differences

light intensity I

A

2

, A = total amplitude amplitude A at a point on the screen A2 = A12 + A2

2 + 2A1A2 cos, = phase difference between A1 and A2 at thepoint

maxima for = 2n minima for = (2n+1) depends on optical path difference : = 2/ interference only for coherent light sources;

two independentlight sources: no interferencesince not coherent (random phase differences)


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Double slit experiment: low intensity

Taylors experiment (1908): double slit experiment with very dimlight: interference pattern emerged after waiting for few weeks

interference cannot be due to interaction between photons, i.e.cannot be outcome of destructive or constructive combination ofphotons

interference pattern is due to some inherent property of eachphoton

it interferes with itself while passing from source to screen

photons dont split light detectors always show signals of same intensity

slits open alternatingly: get two overlapping single-slit diffraction

patterns no two-slit interference add detector to determine through which slit photon goes:

no interference

interference pattern only appears when experiment provides nomeans of determining through which slit photon passes


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double slit experiment with very lowintensity , i.e. one photon or atom at atime:

get still interference pattern if we waitlong enough


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Double slit experiment QM interpretation

patterns on screen are result of distribution ofphotons

no way of anticipating where particular photon willstrike

impossible to tell which path photon took cannotassign specific trajectory to photon

cannot suppose that half went through one slit andhalf through other

can only predict how photons will be distributed onscreen (or over detector(s))

interference and diffraction are statisticalphenomena associated with probability that, in agiven experimental setup, a photon will strike acertain point

high probability bright fringes

low probability

dark fringes


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Double slit expt. -- wave vs quantum

pattern of fringes: Intensity bands due

to variations in squareof amplitude, A2, of

resultant wave oneach point on screen

role of the slits:

to provide two

coherent sources ofthe secondary wavesthat interfere on thescreen

pattern of fringes: Intensity bands due

to variations inprobability, P, of a

photon striking pointson screen

role of the slits:

to present twopotential routes bywhich photon can passfrom source to screen

wave theory quantum theory


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double slit expt., wave function

light intensity at a point on screen I depends on number ofphotons striking the pointnumber of photons probability P of finding photon there, i.e

I P = ||2, = wave function

probability to find photon at a point on the screen :

P = ||2

= |1 + 2|2

= |1|2

+ |2|2

+ 2 |1| |2| cos;

2 |1| |2| cos is interference term; factor cos due to factthat s are complex functions

wave function changes when experimental setup is changed

o by opening only one slit at a timeo by adding detector to determine which path photon took

o by introducing anything which makes paths distinguishable


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Waves or Particles?Youngs double-slitdiffraction experiment

demonstrates the waveproperty of light.

However, dimmingthe light results insingle flashes on the

screen representativeof particles.


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Electron Double-Slit Experiment

C. Jnsson (Tbingen,Germany, 1961) showeddouble-slit interferenceeffects for electrons byconstructing very narrow

slits and using relativelylarge distances between theslits and the observationscreen.

experiment demonstratesthat precisely the samebehavior occurs for bothlight (waves) and electrons(particles).


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Neutrons, A Zeilingeret al. Reviews of

Modern Physics601067-1073 (1988)

He atoms: O Carnal and J MlynekPhysical Review Letters66 2689-

2692 (1991)

C60 molecules: MArndt et al. Nature401, 680-682(1999)

With multiple-slit grating

Without grating

Results on matter wave interference

Interference patterns can not be explained classically - clear demonstration of matter waves

Fringevisibilitydecreases asmolecules are

heated. L.Hackermlleret al. , Nature427 711-714(2004)


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Which slit?

Try to determine which slit the electron went through.

Shine light on the double slit and observe with a microscope. After theelectron passes through one of the slits, light bounces off it; observingthe reflected light, we determine which slit the electron went through.

The photon momentum is:

The electron momentum is:

The momentum of the photons used to determine which slit the electronwent through is enough to strongly modify the momentum of the electronitselfchanging the direction of the electron! The attempt to identifywhich slit the electron passes through will in itself change the diffractionpattern!

Need ph< dto

distinguish the slits.

Diffraction is significantonly when the aperture is ~the wavelength of the wave.


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Discussion/interpretation of double slit experiment

Reduce flux of particles arriving at the slits sothat only one particle arrives at a time. -- still

interference fringes observed! Wave-behavior can be shown by a single atom or photon. Each particle goes through both slits at once. A matter wave can interfere with itself.

Wavelength of matter wave unconnected to anyinternal size of particle -- determined by themomentum

If we try to find out which slit the particle goesthrough the interference pattern vanishes! We cannot see the wave and particle nature at the same

time. If we know which path the particle takes, we lose the

fringes .

Richard Feynman about two-slit experiment: a phenomenon which isimpossible, absolutelyimpossible, to explain in any classical way, and which

has in it the heart of quantum mechanics. In reality it contains the onlymystery.


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Wave particle - duality

So, everything is both a particle and a wave --disturbing!?? Solution: Bohrs Principle of Complementarity:

It is not possible to describe physical observables

simultaneously in terms of both particles andwaves

Physical observables:o quantities that can be experimentally measured. (e.g.

position, velocity, momentum, and energy..)

o in any given instance we must use either the particledescription or the wave description

When were trying to measure particle properties,things behave like particles; when were not, they

behave like waves.


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Probability, Wave Functions, and theCopenhagen Interpretation

Particles are also waves -- described by wavefunction

The wave function determines the probability offinding a particle at a particular position in space at a

given time.

The total probability of finding the particle is 1.

Forcing this condition on the wave function is callednormalization.

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4. Compton Effect-ok