Consider a hypothetical annihilation of a stationary electron with a stationary positron. What is the wavelength of the resulting radiation?

Options

A. `lambda = (h)/(m_(0)c)`
B. `lambda = (2 h)/(m_(0)c^(2))`
C. `lambda = (h)/(2 m_(0)c^(2))`
D. None of these

Answer

A

Explanation

From conservation of momentum, two identical photons travel in opposite direction with equal magnitude of momentum and energy ` hc//lambda`
from conservation of energy , we have
`(hc)/(lambda) + (hc)/(lambda) = m_(0) C^(2) + m_(0) C^(2)`
`lambda = (h)/(m_(0) C)`