The binding energies of the nuclei A and B are `E_(alpha)and E_(alpha)` respectively. Three atoms of the element B fuse to give one atom of element A and an energy Q is released. Then, `E_(a),E_(b)` Q are relaetd as

Options

A. `E_(a)-3E_(b)=Q`
B. `3E_(b)-E_(a)=Q`
C. `E_(a)+3E_(b)=Q`
D. `E_(b)+3E_(a)=Q`

Explanation

To solve the problem, we need to relate the binding energies of nuclei A and B with the energy released during the fusion process. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Binding Energy Concept
Binding energy is the energy required to disassemble a nucleus into its constituent protons and neutrons. A higher binding energy indicates a more stable nucleus.

### Step 2: Identify the Fusion Reaction
The problem states that three atoms of element B fuse to form one atom of element A. We can represent this reaction as:
\[ 3B \rightarrow A \]

### Step 3: Write the Energy Change Equation
The energy released (Q) during the fusion process can be calculated using the binding energies of the reactants and products. The energy released is given by the difference in binding energies of the products and reactants:
\[ Q = \text{(Binding Energy of Products)} - \text{(Binding Energy of Reactants)} \]

### Step 4: Substitute the Binding Energies
For our reaction:
- The binding energy of nucleus A is \( E_A \).
- The binding energy of nucleus B is \( E_B \).

Since three atoms of B are involved, the total binding energy of the reactants is \( 3E_B \). Therefore, we can write:
\[ Q = E_A - 3E_B \]

### Step 5: Rearranging the Equation
Rearranging the equation gives us a relationship between the binding energies and the energy released:
\[ E_A = Q + 3E_B \]

### Conclusion
The relationship between the binding energies \( E_A \), \( E_B \), and the energy released \( Q \) can be summarized as:
\[ E_A = Q + 3E_B \]