Q. Consider a hypothetical annihilation of a stationary electron with a stationary positron. What is the wavelength of resulting radiation ($h =$ Planck’s constant, $c =$ speed of light, $m_{0} =$ rest mass)
A) $\frac{h}{2m_{0}c}$
B) $\frac{h}{m_{0}c}$
C) $\frac{2h}{m_{0}c}$
D) $\frac{h}{m_{0}c^{2}}$
Explanation
(b) From conservation of momentum, two identical photons must travel in opposite directions with equal magnitude of momentum and energy $\frac{hc}{\lambda}$ from conservation of energy $\frac{hc}{\lambda} + \frac{hc}{\lambda} = m_{0}c^{2} + m_{0}c^{2}$
$\Rightarrow \lambda = \frac{h}{m_{0}c}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.