First slide

Energy released in nuclear reactions -Q-value

Question

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

Moderate

A

2.2
B

1.1
C

3.1
D

22

Solution

$\sqrt{2 m k} = \frac{E}{c} \Rightarrow k = \frac{E^{2}}{2 m c^{2}} = \frac{{(7 M e V)}^{2}}{2 \times 24 \times 1.67 \times 10^{- 27} \times {(3 \times 10^{8})}^{2}} = 1.1 K e V$

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