Question

# A radioactive nucleus of mass M emits a photon of frequency v and the nucleus recoils. The recoil energy will be

A
hv
B
Mc2hv
C
h2v22Mc2
D
Zero
Solution
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#### Energy of emitted photon is E=hν For a photon its momentum is given as Energyvelocity of light which is nothing but Ec or hνc According to momentum conservation value of the momentum of recoiled nucleus should also be hνc but in opposite direction to make net momentum zero before and after emission.Now recoil energy E2 = p22M where p is recoil momentum putting p = hνc we get recoil energy as h2ν22Mc2 i.e., option C

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