A certain mass of hydrogen is changed to helium by the process of fusion. The mass defect in fusion reaction is `0.02866 u`. The energy liberated per `u` is
`("given "1 u=931 MeV)`

Options

A. `2.67` Me V
B. `26.7` Me V
C. `6.675` Me V
D. `13.35` Me V

Explanation

To solve the problem, we need to calculate the energy released during the fusion of hydrogen into helium, using the mass defect and the conversion factor for energy per atomic mass unit (u).

### Step-by-Step Solution:

1. **Identify the mass defect**:
The mass defect given in the problem is \( \Delta m = 0.02866 \, u \).

2. **Convert mass defect to energy**:
We know that 1 atomic mass unit (u) is equivalent to 931 MeV. Therefore, the energy released due to the mass defect can be calculated using the formula:
\[ E = \Delta m \times c^2 \]
Here, \( c^2 \) can be replaced by the conversion factor:
\[ E = \Delta m \times 931 \, \text{MeV} \]
Substituting the value of the mass defect:
\[ E = 0.02866 \, u \times 931 \, \text{MeV/u} \]

3. **Calculate the total energy released**:
Performing the multiplication:
\[ E = 0.02866 \times 931 \approx 26.69 \, \text{MeV} \]

4. **Determine the number of nucleons**:
In the fusion process from hydrogen to helium, we consider that helium has 4 nucleons (2 protons and 2 neutrons).

5. **Calculate the binding energy per nucleon**:
To find the binding energy per nucleon, we divide the total energy released by the number of nucleons:
\[ \text{Binding Energy per Nucleon} = \frac{E}{\text{Number of Nucleons}} = \frac{26.69 \, \text{MeV}}{4} \]
\[ \text{Binding Energy per Nucleon} \approx 6.6725 \, \text{MeV} \]

### Final Answer:
The binding energy per nucleon is approximately \( 6.67 \, \text{MeV} \).

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