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)`
(1.) 2.67 MeV
(2.)26.7 MeV
(3.)6.675 MeV
(4.)13.35 MeV

Options

A. `2.67` MeV
B. `26.7` MeV
C. `6.675` MeV
D. `13.35` MeV

Answer

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

### Step-by-Step Solution:

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

2. **Identify the conversion factor**:
We know that \(1 \, u = 931 \, \text{MeV}\).

3. **Calculate the energy liberated using the mass defect**:
The energy liberated (E) can be calculated using the formula:
\[ E = \Delta m \times (931 \, \text{MeV/u}) \]
Substituting the values:
\[ E = 0.02866 \, u \times 931 \, \text{MeV/u} \]

4. **Perform the multiplication**:
\[ E = 0.02866 \times 931 \approx 26.67 \, \text{MeV} \]

5. **Determine the energy per nucleon**:
Since helium has an atomic mass number of 4, we need to find the energy liberated per nucleon:
\[ \text{Energy per nucleon} = \frac{E}{\text{Atomic mass number}} = \frac{26.67 \, \text{MeV}}{4} \]
\[ \text{Energy per nucleon} \approx 6.675 \, \text{MeV} \]

6. **Final answer**:
The energy liberated per nucleon during the fusion reaction is approximately \(6.675 \, \text{MeV}\).

### Conclusion:
The correct answer is option (3) \(6.675 \, \text{MeV}\).

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