Question

The rest mass of a deuteron is equivalent to an energy of 1876 MeV, that of a proton to 939 MeV, and that of a neutron to 940 MeV. A deuteron may disintegrate to a proton and a neutron if it
A.)emits an X-ray photon of energy 2 MeV
B.)captures an X-ray photon of energy 2 MeV
C.)emits an X-ray photon of energy 3 MeV
D.)captures an X-ray photon of energy 3 MeV

Answer 1

Hint: A deuteron is a stable particle and so to disintegrate, it needs to be supplies with energy or say it needs to capture a photon equivalent to its binding energy and that will be the difference in energies of the products after disintegration and that of the deuteron.

Complete step by step solution:
The deuteron is a stable particle composed of a proton and a neutron, so, to disintegrate it, we need to provide a photon with energy equivalent to that of the binding energy of the deuteron.

We have been given that the rest mass of the deuteron is 1876 MeV, that of the proton is 939 MeV and that of the neutron is 940 MeV.

Suppose, Q be the amount of energy equivalent to that of the binding energy required to disintegrate. Thus, the deuteron should capture an X-ray photon and we can write the required equation as follows,

${}_1{H}^2+Q\to {}_1{H}^1{+}_0{H}^1$

$⟹Q=\text{Energy of proton}+\text{Energy of neutron}-\text{Energy of Deuteron}$
$⟹Q=(939MeV+940MeV)-1876MeV=3MeV$

Thus, the deuteron requires to capture an X-ray photon of energy 3MeV to disintegrate.
Hence, option d is the correct answer.

Note: Emittance of photons would have occurred, if the particle had been unstable. But deuteron is one of the three stable isotopes of hydrogen and is often called as the heavy hydrogen and all other isotopes or heavier isotopes emit energy to disintegrate.