The binding energy per nucleon of `O^16` is `7.97 MeV` and that of `O^17` is `7.75 MeV`. The energy (in MeV) required to remove a neutron from `O^17` is.

Options

A. `3.52`
B. `3.64`
C. `4.23`
D. `7.86`

Explanation

To find the energy required to remove a neutron from \( O^{17} \), we can use the concept of binding energy. The binding energy of a nucleus is the energy required to disassemble it into its constituent nucleons.

### Step-by-Step Solution:

1. **Identify the Binding Energies**:
- The binding energy per nucleon of \( O^{16} \) is given as \( 7.97 \, \text{MeV} \).
- The binding energy per nucleon of \( O^{17} \) is given as \( 7.75 \, \text{MeV} \).

2. **Calculate the Total Binding Energy**:
- The total binding energy of \( O^{16} \) (which has 16 nucleons) can be calculated as:
\[ BE_{O^{16}} = 16 \times 7.97 \, \text{MeV} = 127.52 \, \text{MeV} \]
- The total binding energy of \( O^{17} \) (which has 17 nucleons) can be calculated as:
\[ BE_{O^{17}} = 17 \times 7.75 \, \text{MeV} = 131.75 \, \text{MeV} \]

3. **Determine the Energy Required to Remove a Neutron**:
- When a neutron is removed from \( O^{17} \), it transforms into \( O^{16} \) and the energy required to remove that neutron is equal to the difference in binding energy between \( O^{17} \) and \( O^{16} \):
\[ E = BE_{O^{17}} - BE_{O^{16}} = 131.75 \, \text{MeV} - 127.52 \, \text{MeV} = 4.23 \, \text{MeV} \]

4. **Conclusion**:
- The energy required to remove a neutron from \( O^{17} \) is \( 4.23 \, \text{MeV} \).