The binding energy of nucei X and `Y` are `E_(1)` and `E_(2)`, respectively. Two atoms of X fuse to give one atom of `Y` and an energy `Q` is released. Then,

Options

A. `Q=2E_(1)-E_(2)`
B. `Q=E_(2)-2E_(1)`
C. `Qlt2E_(1)-E_(2)`
D. `QgtE_(2)-2E_(1)`

Answer

To solve the problem, we need to analyze the fusion reaction of two atoms of nucleus X into one atom of nucleus Y, and how the binding energies relate to the energy released (Q).

### Step-by-Step Solution:

1. **Identify the Reaction**:
The fusion reaction can be represented as:
\[ 2X \rightarrow Y + Q \]
Here, two nuclei of X combine to form one nucleus of Y and release energy Q.

2. **Understand Binding Energy**:
The binding energy of a nucleus is the energy required to disassemble it into its constituent protons and neutrons. Higher binding energy means a more stable nucleus.

3. **Binding Energies Given**:
Let the binding energy of nucleus X be \(E_1\) and that of nucleus Y be \(E_2\).

4. **Calculate Total Binding Energy of Reactants**:
Since two atoms of X are involved, the total binding energy of the reactants (2X) is:
\[ \text{Total Binding Energy of Reactants} = 2E_1 \]

5. **Calculate Binding Energy of Products**:
The binding energy of the product (Y) is simply:
\[ \text{Binding Energy of Product} = E_2 \]

6. **Determine Energy Released (Q)**:
The energy released during the fusion process can be calculated using the difference in binding energies between the products and the reactants:
\[ Q = \text{Binding Energy of Product} - \text{Total Binding Energy of Reactants} \]
Substituting the values we have:
\[ Q = E_2 - 2E_1 \]

### Final Answer:
Thus, the energy released \(Q\) during the fusion of two atoms of X to form one atom of Y is given by:
\[ Q = E_2 - 2E_1 \]