Question

In Compton scattering, Compton shift equals Compton wavelength if angle of scattering is:

• A. \(0\)
• B. \(\pi/4\)
• C. \(\pi/2\)
• D. \(\pi\)

Hint:

Remember the physical meaning of the limits for Compton scattering: - \(\theta = 0\): No scattering, \(\Delta\lambda = 0\). - \(\theta = \pi/2\) (90 degrees): Shift equals the Compton wavelength, \(\Delta\lambda = \lambda_c\). - \(\theta = \pi\) (180 degrees, backscattering): Maximum shift, \(\Delta\lambda = 2\lambda_c\).

Answer 1

The Correct Option is C

Step 1: State the Compton shift formula. The Compton shift, \(\Delta\lambda\), represents the change in a photon's wavelength after scattering from an electron and is expressed as:\[\Delta\lambda = \frac{h}{m_e c}(1 - \cos\theta)\]where \(\theta\) is the angle of scattering.
Step 2: Define the Compton wavelength. The Compton wavelength, \(\lambda_c\), is a constant given by:\[\lambda_c = \frac{h}{m_e c}\]
Step 3: Equate the Compton shift to the Compton wavelength and solve for \(\theta\). Given \(\Delta\lambda = \lambda_c\), we have:\[\frac{h}{m_e c}(1 - \cos\theta) = \frac{h}{m_e c}\]Dividing both sides by \(\frac{h}{m_e c}\) yields:\[1 - \cos\theta = 1\]\[-\cos\theta = 0\]\[\cos\theta = 0\]The angle \(\theta\) for which \(\cos\theta = 0\) within the range \(0 \le \theta \le \pi\) is \(\theta = \pi/2\).