QB_PH_SEC9_021: Nuclear Properties & Nuclear Forces

The total binding energy of the deuteron nucleus ($^2\text{H}$) is approximately $B = 2.22\text{ MeV}$. Taking atomic mass unit $1\text{ u} = 931.5\text{ MeV}/c^2$, mass of free proton $m_p = 1.00728\text{ u}$, and mass of free neutron $m_n = 1.00866\text{ u}$, what is the atomic mass of the deuteron nucleus in u? (Round off your answer to three decimal places)

Correct Answer

### Step-by-Step Derivation & Verification: 1. **Nuclear Mass Defect Relation**: $B = [m_p + m_n - M_d] c^2 \implies M_d = m_p + m_n - \frac{B}{931.5\text{ MeV/u}}$ 2. **Sum of Constituent Nucleons**: $m_p + m_n = 1.00728\text{ u} + 1.00866\text{ u} = 2.01594\text{ u}$ 3. **Binding Energy Mass Equivalent**: $\Delta m = \frac{2.224\text{ MeV}}{931.5\text{ MeV/u}} = 0.002388\text{ u}$ 4. **Deuteron Mass Computation**: $M_d = 2.01594\text{ u} - 0.00239\text{ u} = 2.01355\text{ u} \approx 2.014\text{ u}$ 5. **Official Range**: $[2.013, 2.015]$.