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

Answer

To find the energy required to remove a neutron from \( O^{17} \), we can use the concept of binding energy. The binding energy per nucleon gives us insight into how tightly the nucleons (protons and neutrons) are bound within the nucleus.

### Step-by-Step Solution:

1. **Identify the binding energies**:
- Binding energy per nucleon of \( O^{16} \) = \( 7.97 \, \text{MeV} \)
- Binding energy per nucleon of \( O^{17} \) = \( 7.75 \, \text{MeV} \)

2. **Write the reaction for removing a neutron**:
\[ O^{17} \rightarrow O^{16} + n \]
Here, \( n \) represents the neutron being removed.

3. **Calculate the total binding energy of the nuclei**:
- For \( O^{16} \):
\[ \text{Total binding energy of } O^{16} = \text{Number of nucleons} \times \text{Binding energy per nucleon} = 16 \times 7.97 \, \text{MeV} = 127.52 \, \text{MeV} \]
- For \( O^{17} \):
\[ \text{Total binding energy of } O^{17} = 17 \times 7.75 \, \text{MeV} = 131.75 \, \text{MeV} \]

4. **Calculate the Q value of the reaction**:
The Q value can be calculated as the difference in binding energies:
\[ Q = \text{Binding energy of } O^{16} - \text{Binding energy of } O^{17} \]
\[ Q = 127.52 \, \text{MeV} - 131.75 \, \text{MeV} = -4.23 \, \text{MeV} \]

5. **Interpret the Q value**:
A negative Q value indicates that energy must be supplied to the system to remove the neutron from \( O^{17} \). Therefore, the energy required to remove a neutron from \( O^{17} \) is \( 4.23 \, \text{MeV} \).

### Final Answer:
The energy required to remove a neutron from \( O^{17} \) is \( 4.23 \, \text{MeV} \).

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