The binding energy per nucleon in O^16 nucleus is (mass of proton = 1.0072 u, mass of neutron = 1.00 — Nuclear Chemistry and Radioactivity Chemistry Question

💡 Solution & Explanation

Step 1 - Nuclear Composition of O-16 $\ce{^{16}_{8}O}$: $Z = 8$ protons, $N = 8$ neutrons, $A = 16$ Step 2 - Calculate Theoretical Mass of Separated Nucleons $$m_{\text{theoretical}} = Z \times m_p + N \times m_n = 8 \times 1.0072 + 8 \times 1.0086\ \text{u}$$ $$= 8.0576 + 8.0688 = 16.1264\ \text{u}$$ Step 3 - Calculate Mass Defect Actual isotopic mass of $\ce{^{16}O} = 16.0000\ \text{u}$: $$\delta m = m_{\text{theoretical}} - m_{\text{actual}} = 16.1264 - 16.0000 = 0.1264\ \text{u}$$ Step 4 - Calculate Total Binding Energy $$E_b = \delta m \times 931.5\ \text{MeV/u} = 0.1264 \times 931.5 = 117.7\ \text{MeV}$$ Step 5 - Binding Energy Per Nucleon $$\frac{E_b}{A} = \frac{117.7}{16} = \boxed{7.36\ \text{MeV/nucleon}}$$ Step 6 - Evaluate Options - **(A) 14.72 MeV**: This is $E_b/A$ using only 8 nucleons (wrong denominator). Incorrect. - **(B) 7.36 MeV**: Matches our calculation. **Correct.** - **(C) 117.7 MeV**: This is the total binding energy, not per nucleon. Incorrect. - **(D) 4.8 MeV**: Incorrect. $$\boxed{\text{Answer: B — 7.36 MeV per nucleon}}$$