Question

A free nucleus of mass $24amu$ emits a gamma photon (when initially at rest). The energy of the photon is $7MeV$. The recoil energy of the nucleus in $keV$ is

• A. $2.2$
• B. $1.1$
• C. $3.1$
• D. $22$

Answer 1

The correct option is B $1.1$

$E=\frac{p^2}{2m}$

Conservation of momentum for photon:
$E=\frac{hc}{\lambda }=7MeV$
$p=\frac{h}{\lambda }=7/cMeV$

Equating the momentum:
$\frac{7}{c}=\sqrt{2E_{nucleus}m}$

Substitute $m=24amu$,
Solving with appropriate units:
$E_{nucleus}=1.1KeV$