[UPSC CSE 2025] Nuclear Physics (Q7, 15M)

The total binding energies of ${}_8^{15}\text{O}$ , ${}_8^{16}\text{O}$ and ${}_8^{17}\text{O}$ are $111\cdot 96 \text{ MeV}$ , $127\cdot 62 \text{ MeV}$ and $131\cdot 76 \text{ MeV}$ respectively. Determine the energy gap between $1p_{1/2}$ and $1d_{5/2}$ neutron shells for the nuclide whose mass number is close to $16$ .