Discussion
The ratio \(\frac{\delta({}^{15}_{7}\mathrm{N})}{\delta({}^{256}_{100}\mathrm{Fm})}\), where \(\delta\) denotes the pairing term in the Semi-empirical mass formula (Weizsäcker formula) for binding energy, is :
Answer: D
The ratio is 0.
The pairing term depends on whether the proton and neutron numbers are even or odd:
- odd \(A\): \(\delta = 0\);
- even \(Z\), even \(N\): \(\delta = +a_{p}A^{-1/2}\) (or a similar power of \(A\));
- odd \(Z\), odd \(N\): \(\delta = -a_{p}A^{-1/2}\).
\({}^{15}_{7}\mathrm{N}\) has odd mass number (\(Z = 7\), \(N = 8\)), so its pairing term is zero. \({}^{256}_{100}\mathrm{Fm}\) has \(Z = 100\) and \(N = 156\), both even, so its pairing term is non-zero. The ratio is therefore 0.
Non-zero values such as \(\pm 4\) or \(\pm 8\) could only arise if both nuclei had non-zero pairing terms, comparing their \(A^{-1/2}\) factors, which is not the case here.
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