Tag: gamma decay

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Multiple choice gamma decay change in nucleus due to radioactive decay alpha, beta and gamma particles (rays) and their properties

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

  1. $2.2$
  2. $1.1$
  3. $3.1$
  4. $22$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

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

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

Equating the momentum:
$ \cfrac{7}{c }= \sqrt{2E _{nucleus}m}$

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