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Physics / Sears and Zemansky's University Physics with Modern Physics 13 / Chapter 38 / Problem 13DQ

Sears and Zemansky's University Physics with Modern Physics | 13th Edition | ISBN: 9780321696861 | Authors: Hugh D. Young; Roger A. Freedman; A. Lewis Ford

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A photon of frequency f undergoes Compton scattering from

Chapter 38, Problem 13DQ

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QUESTION:

A photon of frequency f undergoes Compton scattering from an electron at rest and scatters through an angle Φ. The frequency of the scattered photon is f’. How is f’ related to f? Does your answer depend on Φ? Explain.

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QUESTION:

A photon of frequency f undergoes Compton scattering from an electron at rest and scatters through an angle Φ. The frequency of the scattered photon is f’. How is f’ related to f? Does your answer depend on Φ? Explain.

ANSWER:

Introduction

We have to find out the relationship between the frequency $f$ and $f'$ for compton scattering. Then we have to discuss why it depends on the angle of scattering $\phi{}$ .

Step 1

If $\lambda{}$ and $\lambda{}'$ are the wavelength of light corresponding to the frequency $f$ and $f'$ respectively, then the relationship between them is given by

$\lambda{}'-\lambda{}=\frac{h}{mc}(1-\cos{}\phi{})$ (1)

Now we know that

$\lambda{}=\frac{c}{f}$ and $\lambda{}'=\frac{c}{f'}$

Now putting this values in equation (1) we have

$\frac{c}{f'}-\frac{c}{f}=\frac{h}{mc}(1-\cos{}\phi{})$

$\frac{1}{f'}-\frac{1}{f}=\frac{h}{m{c}^{2}}(1-\cos{}\phi{})$ (2)

Equation (2) represents the relationship between $f$ and $f'$ .

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