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Question

The rest mass of a deuteron 1H2 is equivalent to an energy of 1876 MeV, the rest mass of a proton is equivalent to 939 MeV and that of a neutron is 940 MeV. A deuteron may disintegrate to a proton and a neutron if it

A
emits a γ-rays photon of energy 2 MeV.
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B
captures a γ-rays photon of energy 2 MeV.
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C
emits a γ-ray photon of energy 3 MeV.
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D
captures a γ-ray photon of energy 3 MeV.
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Solution

The correct option is D captures a γ-ray photon of energy 3 MeV.
Given that, the rest mass energy of Deuteron

E[1H2]=1876 MeV

The total rest mass energy of proton and neutron,

E(p+n)=Ep+En=939 MeV+940 MeV

E(p+n)=1879 MeV

ΔE=E(p+n)E[1H2]=3 MeV

As E(p+n)>E[1H2], a deuteron should capture a γ-rays photon of energy 3 MeV to disintegrate into a proton and a neutron.

Hence, option (D) is correct.

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