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.

Answer

To find the energy required to remove a neutron from \( O^{17} \), we can follow these steps:

### Step 1: Understand Binding Energy
The binding energy of a nucleus is the energy required to disassemble it into its constituent nucleons (protons and neutrons). The binding energy per nucleon gives us an idea of how tightly bound the nucleons are within the nucleus.

### Step 2: Calculate Total Binding Energy of \( O^{17} \)
The binding energy per nucleon for \( O^{17} \) is given as \( 7.75 \, \text{MeV} \). Since \( O^{17} \) has 17 nucleons (16 protons and 1 neutron), the total binding energy \( BE_{O^{17}} \) can be calculated as:
\[ BE_{O^{17}} = \text{Binding Energy per Nucleon} \times \text{Number of Nucleons} = 7.75 \, \text{MeV} \times 17 \]

### Step 3: Calculate Total Binding Energy of \( O^{16} \)
The binding energy per nucleon for \( O^{16} \) is given as \( 7.97 \, \text{MeV} \). Since \( O^{16} \) has 16 nucleons, the total binding energy \( BE_{O^{16}} \) can be calculated as:
\[ BE_{O^{16}} = 7.97 \, \text{MeV} \times 16 \]

### Step 4: Calculate the Energy Required to Remove a Neutron
The energy required to remove a neutron from \( O^{17} \) is equal to the difference in binding energy between \( O^{17} \) and \( O^{16} \):
\[ \text{Energy required} = BE_{O^{17}} - BE_{O^{16}} \]

### Step 5: Perform the Calculations
1. Calculate \( BE_{O^{17}} \):
\[ BE_{O^{17}} = 7.75 \, \text{MeV} \times 17 = 131.75 \, \text{MeV} \]

2. Calculate \( BE_{O^{16}} \):
\[ BE_{O^{16}} = 7.97 \, \text{MeV} \times 16 = 127.52 \, \text{MeV} \]

3. Calculate the energy required to remove a neutron:
\[ \text{Energy required} = 131.75 \, \text{MeV} - 127.52 \, \text{MeV} = 4.23 \, \text{MeV} \]

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

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