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: Recall the formula for the Compton shift. The Compton shift, \(\Delta\lambda\), which is the change in wavelength of a photon after scattering off an electron, is given by: \[ \Delta\lambda = \frac{h}{m_e c}(1 - \cos\theta) \] where \(\theta\) is the scattering angle.
Step 2: Define the Compton wavelength. The Compton wavelength, \(\lambda_c\), is a constant defined as: \[ \lambda_c = \frac{h}{m_e c} \]
Step 3: Set the Compton shift equal to the Compton wavelength and solve for \(\theta\). We are given the condition \(\Delta\lambda = \lambda_c\). \[ \frac{h}{m_e c}(1 - \cos\theta) = \frac{h}{m_e c} \] Dividing both sides by \(\frac{h}{m_e c}\) gives: \[ 1 - \cos\theta = 1 \] \[ -\cos\theta = 0 \] \[ \cos\theta = 0 \] The angle \(\theta\) for which \(\cos\theta = 0\) (in the range \(0 \le \theta \le \pi\)) is \(\theta = \pi/2\).