Question

An atom of mass $M$ which is in the state of rest emits a photon of wavelength $\lambda$. As a result, the atom will deflect with the kinetic energy equal to $(h$ is Planck's constant)

• A. $ \frac{h^{2}}{M\lambda ^{2}}$
• B. $ \frac{1}{2}\frac{h^{2}}{M\lambda ^{2}}$
• C. $ \frac{h}{M\lambda } $
• D. $ \frac{1}{2}\frac{h}{M\lambda } $

Answer 1

Answer: (B)

Momentum of photon, $p=\frac{h}{\lambda}$
Kinetic energy of photon of mass
$M, K=\frac{p^{2}}{2 M}$
or $K=\frac{h^{2}}{2 M \lambda^{2}}$