Question

The rest mass of a deuteron ${}_1{\text{H}}^2$ is equivalent to an energy of $1876\text{MeV}$, the rest mass of a proton is equivalent to $939\text{MeV}$ and that of a neutron is $940\text{MeV}$. A deuteron may disintegrate to a proton and a neutron if it

• A. emits a $\gamma$-rays photon of energy $2\text{MeV}$.
• B. captures a $\gamma$-rays photon of energy $2\text{MeV}$.
• C. emits a $\gamma$-ray photon of energy $3\text{MeV}$.
• D. captures a $\gamma$-ray photon of energy $3\text{MeV}$.

Answer 1

The correct option is D captures a $\gamma$-ray photon of energy $3\text{MeV}$.

Given that, the rest mass energy of Deuteron

$E\left[{}_1{\text{H}}^2\right]=1876\text{MeV}$

The total rest mass energy of proton and neutron,

$E_{(p+n)}=E_p+E_n=939\text{MeV}+940\text{MeV}$

$\Rightarrow E_{(p+n)}=1879\text{MeV}$

$\Delta E=E_{(p+n)}-E\left[{}_1{\text{H}}^2\right]=3\text{MeV}$

As $E_{(p+n)}>E\left[{}_1{\text{H}}^2\right]$, a deuteron should capture a $\gamma$-rays photon of energy $3\text{MeV}$ to disintegrate into a proton and a neutron.

Hence, option $\left(D\right)$ is correct.