The source of energy of stars is nuclear fusion. Fusion reaction occurs at very high temperature, about `10^(7) `. Energy released in the process of fusion is due to mass defect. It is also called `Q`-value. `Q = Delta mc^(2), Delta m =` mass defect.
The binding energy per nucleon of `._(1)H^(2)` and `._(2)He^(4)` are `1.1 MeV` and `7 MeV`, respectively. If two deuteron nuclei react to form a single helium nucleus, then the energy released is

Options

A. `13.9 MeV`
B. `26.9 MeV`
C. `23.6 MeV`
D. `19.3 MeV`

Explanation

To solve the problem, we need to calculate the energy released when two deuteron nuclei react to form a single helium nucleus. We will use the binding energy per nucleon values provided for deuterium and helium.

### Step-by-Step Solution:

1. **Identify the Binding Energy per Nucleon:**
- For deuterium (D or \( _{1}^{2}H \)), the binding energy per nucleon is given as \( 1.1 \, \text{MeV} \).
- For helium (He or \( _{2}^{4}He \)), the binding energy per nucleon is given as \( 7 \, \text{MeV} \).

2. **Calculate the Total Binding Energy of Deuterium:**
- Each deuterium nucleus has 2 nucleons (1 proton and 1 neutron).
- Total binding energy for one deuterium nucleus = \( 2 \, \text{nucleons} \times 1.1 \, \text{MeV/nucleon} = 2.2 \, \text{MeV} \).
- Since we have two deuterium nuclei, the total binding energy for both = \( 2 \times 2.2 \, \text{MeV} = 4.4 \, \text{MeV} \).

3. **Calculate the Total Binding Energy of Helium:**
- The helium nucleus has 4 nucleons (2 protons and 2 neutrons).
- Total binding energy for helium = \( 4 \, \text{nucleons} \times 7 \, \text{MeV/nucleon} = 28 \, \text{MeV} \).

4. **Calculate the Energy Released (Q-value):**
- The energy released in the fusion reaction is the difference between the total binding energy of the products (helium) and the total binding energy of the reactants (deuterium).
- Energy released \( Q = \text{Binding energy of He} - \text{Total binding energy of 2 D} \)
- \( Q = 28 \, \text{MeV} - 4.4 \, \text{MeV} = 23.6 \, \text{MeV} \).

5. **Final Answer:**
- The energy released when two deuteron nuclei react to form a single helium nucleus is \( 23.6 \, \text{MeV} \).