Consider the following nuclear reaction, `X^200rarrA^110+B^90+En ergy`
If the binding energy per nucleon for X, A and B are 7.4 MeV, 8.2 MeV and 8.2 MeV respectively, the energy released will be

Options

A. (a) 900 MeV
B. (b) 110 MeV
C. (c) 200 MeV
D. (d) 160 MeV

Explanation

To find the energy released in the nuclear reaction \( X^{200} \rightarrow A^{110} + B^{90} + \text{Energy} \), we will follow these steps:

### Step 1: Identify the binding energy per nucleon
We are given the binding energy per nucleon for the following nuclei:
- For nucleus \( X \): 7.4 MeV
- For nucleus \( A \): 8.2 MeV
- For nucleus \( B \): 8.2 MeV

### Step 2: Calculate the total binding energy of the initial nucleus \( X \)
The total number of nucleons in \( X \) is 200. Therefore, the total binding energy of \( X \) can be calculated as:
\[ \text{Total Binding Energy of } X = \text{Binding Energy per Nucleon} \times \text{Number of Nucleons} \]
\[ = 7.4 \, \text{MeV/nucleon} \times 200 \, \text{nucleons} = 1480 \, \text{MeV} \]

### Step 3: Calculate the total binding energy of the final products \( A \) and \( B \)
- For nucleus \( A \) (110 nucleons):
\[ \text{Total Binding Energy of } A = 8.2 \, \text{MeV/nucleon} \times 110 \, \text{nucleons} = 902 \, \text{MeV} \]
- For nucleus \( B \) (90 nucleons):
\[ \text{Total Binding Energy of } B = 8.2 \, \text{MeV/nucleon} \times 90 \, \text{nucleons} = 738 \, \text{MeV} \]

### Step 4: Calculate the total binding energy of the final products
Now, we add the binding energies of \( A \) and \( B \):
\[ \text{Total Binding Energy of Final Products} = 902 \, \text{MeV} + 738 \, \text{MeV} = 1640 \, \text{MeV} \]

### Step 5: Calculate the energy released in the reaction
The energy released in the reaction is given by the difference in binding energy between the final products and the initial nucleus:
\[ \text{Energy Released} = \text{Total Binding Energy of Final Products} - \text{Total Binding Energy of } X \]
\[ = 1640 \, \text{MeV} - 1480 \, \text{MeV} = 160 \, \text{MeV} \]

### Final Answer
The energy released in the reaction is \( 160 \, \text{MeV} \).

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