Consider the nuclear reaction `X^(200)toA^(110)+B^(80)+Q`. If the binding energy per nucleon for X, A and B are 7.4 MeV, 8.2 MeV and 8.1 MeV respectively, then the energy released in the reaction:

Options

A. 70 MeV
B. 200 MeV
C. 190 MeV
D. 10 MeV

Answer

To solve the problem, we need to calculate the energy released in the nuclear reaction given the binding energy per nucleon of the involved nuclei. The energy released can be calculated using the formula:

\[ Q = \text{Final Binding Energy} - \text{Initial Binding Energy} \]

### Step 1: Calculate the Initial Binding Energy of X

The initial nucleus \(X\) has a mass number of 200 and a binding energy per nucleon of 7.4 MeV.

\[ \text{Initial Binding Energy} = \text{Number of Nucleons} \times \text{Binding Energy per Nucleon} \]
\[ \text{Initial Binding Energy} = 200 \times 7.4 \text{ MeV} = 1480 \text{ MeV} \]

### Step 2: Calculate the Final Binding Energy of A and B

For nucleus \(A\) with a mass number of 110 and a binding energy per nucleon of 8.2 MeV:

\[ \text{Binding Energy of A} = 110 \times 8.2 \text{ MeV} = 902 \text{ MeV} \]

For nucleus \(B\) with a mass number of 80 and a binding energy per nucleon of 8.1 MeV:

\[ \text{Binding Energy of B} = 80 \times 8.1 \text{ MeV} = 648 \text{ MeV} \]

### Step 3: Calculate the Total Final Binding Energy

Now, we sum the binding energies of nuclei \(A\) and \(B\):

\[ \text{Total Final Binding Energy} = \text{Binding Energy of A} + \text{Binding Energy of B} \]
\[ \text{Total Final Binding Energy} = 902 \text{ MeV} + 648 \text{ MeV} = 1550 \text{ MeV} \]

### Step 4: Calculate the Energy Released in the Reaction

Now we can find the energy released \(Q\):

\[ Q = \text{Total Final Binding Energy} - \text{Initial Binding Energy} \]
\[ Q = 1550 \text{ MeV} - 1480 \text{ MeV} = 70 \text{ MeV} \]

### Final Answer

The energy released in the reaction is:

\[ \boxed{70 \text{ MeV}} \]