Question

What is the Compton shift for a photon backscattered at 180 degrees?

• A. $\frac{h}{mc}$
• B. $\frac{2h}{mc}$
• C. $\frac{h}{2mc}$
• D. $0$

Hint:

Remember: Maximum Compton shift occurs at $180^\circ$ → $\frac{2h}{mc}$.

Answer 1

The Correct Option is B

Concept: Compton shift refers to the change in wavelength of a photon when it is scattered by a particle such as an electron.
Step 1: Compton shift formula.
\[ \Delta \lambda = \frac{h}{mc}(1 - \cos \theta) \]
Step 2: Given condition.
For backscattering, $\theta = 180^\circ$ \[ \cos 180^\circ = -1 \]
Step 3: Substitute the value.
\[ \Delta \lambda = \frac{h}{mc}(1 - (-1)) = \frac{h}{mc}(2) \] \[ \Delta \lambda = \frac{2h}{mc} \]
Step 4: Evaluating the options.

• $\frac{h}{mc}$ $\rightarrow$ Incorrect
• $\frac{2h}{mc}$ $\rightarrow$ Correct
• $\frac{h}{2mc}$ $\rightarrow$ Incorrect
• $0$ $\rightarrow$ Incorrect

Step 5: Conclusion.
Thus, the Compton shift for backscattering is $\frac{2h}{mc}$.