What is the energy required for separation of an O^16 nucleus into four identical particles? (Nuclea — Nuclear Chemistry and Radioactivity Chemistry Question

💡 Solution & Explanation

Step 1 - Write the Separation Reaction $$\ce{^{16}_{8}O -> 4^{4}_{2}He}$$ Step 2 - Calculate Mass Defect Given nuclear masses: - $m(\ce{^{16}O}) = 15.9944\ \text{u}$ - $m(\ce{^{4}He}) = 4.0026\ \text{u}$ Mass of products: $$4 \times m(\ce{^{4}He}) = 4 \times 4.0026 = 16.0104\ \text{u}$$ Mass defect (energy must be supplied, so products are heavier than reactant): $$\delta m = m(\text{products}) - m(\text{reactant}) = 16.0104 - 15.9944 = 0.0160\ \text{u}$$ Step 3 - Convert to Energy Using $1\ \text{u} = 931.5\ \text{MeV}$: $$E = \delta m \times 931.5 = 0.0160 \times 931.5 = \boxed{14.904\ \text{MeV}}$$ Step 4 - Evaluate Options - **(A) 14.904 MeV**: Matches our calculation. **Correct.** - **(B) 0.9315 MeV**: Corresponds to $\delta m = 0.001\ \text{u}$, which is 1/16 of the correct value. Incorrect. - **(C) 1.863 MeV**: Twice option B — likely a wrong factor applied. Incorrect. - **(D) 698.15 MeV**: Enormously too large — likely calculated using total atomic mass rather than nuclear mass difference. Incorrect. $$\boxed{\text{Answer: A — 14.904 MeV}}$$