Question

A photon of frequency \( \nu \) strikes an electron of mass \( m \) initially at rest. After scattering at an angle \( \phi \), the photon loses half of its energy. If the electron recoils at an angle \( \theta \), which of the following is (are) true?

• A. \( \cos\phi = \left( 1 - \frac{mc^2}{h\nu} \right) \)
• B. \( \sin\theta = \left( 1 - \frac{mc^2}{h\nu} \right) \)
• C. The ratio of the magnitudes of momenta of the recoiled electron and scattered photon is \( \frac{\sin\phi}{\sin\theta} \)
• D. Change in photon wavelength is \( \frac{h}{mc} (1 - 2 \cos\phi) \)

Hint:

In Compton scattering, the momenta of the scattered photon and recoiled electron are related by the angles of scattering, and the energy loss depends on the photon’s initial energy and the scattering angle.

Answer 1

The Correct Option is C

Step 1: Understanding the photon-electron interaction.
In Compton scattering, when a photon scatters off an electron, the energy transferred to the electron depends on the angle of scattering. The relationship between the momenta of the electron and photon can be derived from conservation of momentum and energy. The correct expression for the ratio of the magnitudes of the momenta is \( \frac{\sin\phi}{\sin\theta} \), which follows from the geometry of the scattering.
Step 2: Conclusion.
Thus, the correct answer is option (C).