Binding energy per nucleon of fixed nucleus `X^(A)` is `6 MeV`. It absorbs a neutron moving with `KE= 2 MeV` and converts into Y at ground state, emitting a photon of energy `1 MeV`. The Binding energy per nucleon of Y (in MeV) is -

Options

A. `((6A+1))/((A+1))`
B. `((6A-1))/((A+1))`
C. 7
D. can not be determined

Explanation

To solve the problem, we need to calculate the binding energy per nucleon of nucleus Y after it absorbs a neutron and emits a photon. Here are the steps to arrive at the solution:

### Step 1: Understand the Binding Energy of Nucleus X
The binding energy per nucleon of nucleus \( X^{(A)} \) is given as \( 6 \, \text{MeV} \). The total binding energy \( BE_X \) of nucleus \( X \) can be calculated as:
\[ BE_X = 6 \, \text{MeV} \times A \]
where \( A \) is the mass number of nucleus \( X \).

### Step 2: Determine the Energy Changes During the Reaction
Nucleus \( X \) absorbs a neutron with a kinetic energy of \( 2 \, \text{MeV} \) and emits a photon of energy \( 1 \, \text{MeV} \). The net change in binding energy \( BE_Y \) for nucleus \( Y \) can be calculated as follows:
\[ BE_Y = BE_X + \text{(Energy absorbed)} - \text{(Energy emitted)} \]
Substituting the values:
\[ BE_Y = 6A + 2 - 1 = 6A + 1 \, \text{MeV} \]

### Step 3: Calculate the Binding Energy per Nucleon of Nucleus Y
After the absorption of a neutron, the mass number of nucleus \( Y \) becomes \( A + 1 \). Therefore, the binding energy per nucleon \( BE_{per nucleon} \) for nucleus \( Y \) is given by:
\[ BE_{per nucleon} = \frac{BE_Y}{A + 1} \]
Substituting the expression for \( BE_Y \):
\[ BE_{per nucleon} = \frac{6A + 1}{A + 1} \]

### Final Answer
Thus, the binding energy per nucleon of nucleus \( Y \) is:
\[ \frac{6A + 1}{A + 1} \, \text{MeV} \]