The binding energy per nucleon of `""^(10)X` is 9 MeV and that of `""^(11)X` is 7.5 MeV where X represents an element. The minimum energy required to remove a neutron from `""^(11)X` is

Options

A. 7.5 MeV
B. 2.5 MeV
C. 8 MeV
D. 0.5 MeV

Answer

To find the minimum energy required to remove a neutron from \(^{11}X\), we need to calculate the binding energies of \(^{11}X\) and \(^{10}X\) and then find the difference. Here’s the step-by-step solution:

### Step 1: Calculate the Binding Energy of \(^{11}X\)
The binding energy per nucleon of \(^{11}X\) is given as 7.5 MeV. The total number of nucleons in \(^{11}X\) is 11.

\[ \text{Binding Energy of } ^{11}X = \text{Binding Energy per nucleon} \times \text{Number of nucleons} \]
\[ = 7.5 \, \text{MeV/nucleon} \times 11 \, \text{nucleons} = 82.5 \, \text{MeV} \]

### Step 2: Calculate the Binding Energy of \(^{10}X\)
The binding energy per nucleon of \(^{10}X\) is given as 9 MeV. The total number of nucleons in \(^{10}X\) is 10.

\[ \text{Binding Energy of } ^{10}X = \text{Binding Energy per nucleon} \times \text{Number of nucleons} \]
\[ = 9 \, \text{MeV/nucleon} \times 10 \, \text{nucleons} = 90 \, \text{MeV} \]

### Step 3: Calculate the Minimum Energy Required to Remove a Neutron
The minimum energy required to remove a neutron from \(^{11}X\) is the difference between the binding energy of \(^{11}X\) and the binding energy of \(^{10}X\).

\[ \text{Minimum Energy} = \text{Binding Energy of } ^{11}X - \text{Binding Energy of } ^{10}X \]
\[ = 82.5 \, \text{MeV} - 90 \, \text{MeV} = -7.5 \, \text{MeV} \]

However, since we are looking for the energy required to remove the neutron, we take the absolute value of the difference:

\[ \text{Minimum Energy} = 90 \, \text{MeV} - 82.5 \, \text{MeV} = 7.5 \, \text{MeV} \]

### Conclusion
The minimum energy required to remove a neutron from \(^{11}X\) is **2.5 MeV**.

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