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1. Science
2. Advanced Physics
3. Advanced Physics questions and answers
4. EE1102Quantum PhysicsAY2324 S2AssignmentInstructions:The assignment has 4
questions and is worth 100 marks in totalPlease show full, step-by-step
working and reasoning to earn full creditThe Compton shift equation is the
shift in the photon wavelength after it scatters off an electron at rest.
The photon in question, however, is in vacuum. In this
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* QUESTION: EE1102QUANTUM PHYSICSAY2324 S2ASSIGNMENTINSTRUCTIONS:THE
ASSIGNMENT HAS 4 QUESTIONS AND IS WORTH 100 MARKS IN TOTALPLEASE SHOW FULL,
STEP-BY-STEP WORKING AND REASONING TO EARN FULL CREDITTHE COMPTON SHIFT
EQUATION IS THE SHIFT IN THE PHOTON WAVELENGTH AFTER IT SCATTERS OFF AN
ELECTRON AT REST. THE PHOTON IN QUESTION, HOWEVER, IS IN VACUUM. IN THIS
EE1102
Quantum Physics
AY2324 S2
Assignment
Instructions:
The assignment has 4 questions and is worth 100 marks in total
Please show full, step-by-step working and reasoning to earn full credit
The Compton shift equation is the shift in the photon wavelength after it
scatters off an electron at rest. The photon in question, however, is in
vacuum. In this assignment, we will explore the case where the incident and
outgoing photons are in a non-vacuum medium.
Figure 1: Compton scattering
In a medium of refractive index n, the wavelength of light λ0 is related to
its frequency f0 via the relation λ0=cnf0, where c is the speed of light
in vacuum. Fig. 1 is labelled with variables of relevance, including input
photon frequency f, outgoing photon angle θ, outgoing photon frequency f',
outgoing electron angle φ, outgoing electron energy E and outgoing
electron momentum p. In this problem, the momenta of all particles, before
and after, lie entirely in the plane of the paper.
Write the energy conservation equation and the momentum conservation
equations for Compton scattering for incident and outgoing photons in a
medium of refractive index n. Explain your answer in detail.
[20 marks]
Solve the equations to obtain the outgoing photon frequency f' in the
following form:
f'=(-B+-B2-4AC2)2A
where you are to determine the unknowns A,B and C in terms of f,c,n,θ, and
electron rest mass m. You may use the fact that for general (relativistic)
electrons, the dispersion relation is E=p2c2+m2c42.
[40 marks]
3. Show that your result in Question 2 is consistent with the Compton shift
formula presented in lecture when n=1.
[20 marks]
4. Let the percentage change in the photon energy be defined as
(Question 4 continued on page 2)
1
EE1102
Quantum Physics
AY2324 S2
Percentage change
-= final photon energy - initial photon energy initial photon energy ×100%,
where the final photon energy refers is being collected at observation angle
θ=180°. For incident light at photon energy 1eV and in air ( n=1 ), what
is the percentage change in the photon energy? How does this value change
when silicon =(3.5 is used as the medium instead? You may assume that the
observer is also in the medium. Comment on how this percentage change varied
when we went from n=1 to n=3.5.
[20 marks]
For your reference:
Fundamental constants (high precision)
Planck's constant h=6.62607015×10-34Js
Elementary charge e=1.602176634×10-19C
Electron mass m=9.1093837015×10-31kg
Speed of light c=299,792,458ms
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Question 1: Energy and Momentum Conservation Equations
In Compton scattering, both energy and momentu...
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