The total binding energy of $\,^{16}_{8}\mathrm{O}$ is approximately $127.6\,\text{MeV}$. Its binding energy per nucleon is closest to
A$8.0\,\text{MeV}$
B$7.0\,\text{MeV}$
C$15.9\,\text{MeV}$
D$931\,\text{MeV}$
Answer & Solution
Correct answer: A. $8.0\,\text{MeV}$
1. Binding energy per nucleon $E_{bn} = E_b / A$, where $A$ is the mass number.
2. For $\,^{16}_{8}\mathrm{O}$, $A = 16$.
3. $E_{bn} = 127.6 / 16 = 7.975\,\text{MeV}$ per nucleon, which rounds to $8.0\,\text{MeV}$.
4. This is very close to the typical mid-mass nuclear value of $\sim 8.5\,\text{MeV}/\text{nucleon}$ — oxygen sits on the rapidly-rising part of the binding-energy curve.
5. Option A would be the value for light nuclei (e.g. $\,^{4}\mathrm{He}$ has $E_{bn} \approx 7.1\,\text{MeV}$). Option C is double the correct value (forgot to divide by 2 somewhere). Option D is the energy equivalent of $1\,u$ — confusing TWO different physical quantities.
_Source: NCERT Class 12 Physics Part 2, Ch 13, §13.4 (Binding energy / nucleon, Fig. 13.1 + Example 13.3), p. 5–6._
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