The binding energy per nucleon of `._(5)B^(10)` is 8 MeV and that of `._(5)B^(11)` is 7.5 MeV. The energy required to remove a neutron from `._(5)B^(11)` is (mass of electron and proton are `9.11 xx 10^(-21) kg` and `1.67 xx 10^(-27) kg` respectively.

Options

A. `2.5 MeV`
B. `8.0 MeV`
C. `0.5 MeV`
D. `7.5 MeV`

Explanation

To find the energy required to remove a neutron from the boron isotope \( _{5}^{11}B \), we can follow these steps:

### Step 1: Understand the Binding Energy
The binding energy per nucleon for \( _{5}^{11}B \) is given as 7.5 MeV. This means that the total binding energy for \( _{5}^{11}B \) can be calculated by multiplying the binding energy per nucleon by the total number of nucleons (which is 11 for \( _{5}^{11}B \)).

\[ \text{Total Binding Energy of } _{5}^{11}B = \text{Binding Energy per Nucleon} \times \text{Number of Nucleons} \]
\[ = 7.5 \, \text{MeV} \times 11 = 82.5 \, \text{MeV} \]

### Step 2: Calculate the Binding Energy for \( _{5}^{10}B \)
The binding energy per nucleon for \( _{5}^{10}B \) is given as 8 MeV. Similarly, we calculate the total binding energy for \( _{5}^{10}B \):

\[ \text{Total Binding Energy of } _{5}^{10}B = 8 \, \text{MeV} \times 10 = 80 \, \text{MeV} \]

### Step 3: Find the Energy Required to Remove a Neutron
The energy required to remove a neutron from \( _{5}^{11}B \) can be found by taking the difference between the total binding energy of \( _{5}^{11}B \) and \( _{5}^{10}B \):

\[ \text{Energy required to remove a neutron} = \text{Total Binding Energy of } _{5}^{11}B - \text{Total Binding Energy of } _{5}^{10}B \]
\[ = 82.5 \, \text{MeV} - 80 \, \text{MeV} = 2.5 \, \text{MeV} \]

### Final Answer
The energy required to remove a neutron from \( _{5}^{11}B \) is **2.5 MeV**.

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