The atomic mass of a deuteron (${}^2\text{H}$) is $2.014102\text{u}$. The masses of a proton and a neutron are $1.007276\text{u}$ and $1.008665\text{u}$ respectively. Using $1\text{u}=931.5\text{MeV}/c^2$, calculate the binding energy per nucleon of the deuteron nucleus.

Step-by-step solution

1. Write the mass defect: $\Delta m=(m_p+m_n)-m_{\text{deuteron}}$.
2. Substitute the given values: $\Delta m=(1.007276+1.008665)-2.014102=0.001839\text{u}$.
3. Convert the mass defect to energy: $E=\Delta m\times 931.5\text{MeV}=0.001839\times 931.5=1.712\text{MeV}$.
4. Deuteron has two nucleons, so binding energy per nucleon $=\frac{1.712}{2}=0.856\text{MeV}$.
5. Round to three significant figures: $0.856\text{MeV}\approx 0.86\text{MeV}$.

Concept tested: Binding energy per nucleon

Published 19 September 2026 · How this solution was prepared and checked