The mass defect for the nucleus of helium is `0.0303` a.m.u. What is the binding energy per nucleon for helium in `MeV` ?

Options

A. 28
B. 7
C. 4
D. 1

Explanation

To find the binding energy per nucleon for the helium nucleus given its mass defect, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the mass defect**:
The mass defect for the helium nucleus is given as \( \Delta m = 0.0303 \, \text{a.m.u.} \).

2. **Convert mass defect to energy**:
The energy equivalent of the mass defect can be calculated using the formula:
\[ E = \Delta m \times 931 \, \text{MeV} \]
where \( 931 \, \text{MeV} \) is the energy equivalent of 1 a.m.u.

3. **Calculate the total binding energy**:
Substitute the mass defect value into the equation:
\[ E = 0.0303 \, \text{a.m.u.} \times 931 \, \text{MeV/a.m.u.} = 28.24 \, \text{MeV} \]

4. **Determine the number of nucleons in helium**:
Helium has 2 protons and 2 neutrons, so the total number of nucleons \( A \) is:
\[ A = 2 + 2 = 4 \]

5. **Calculate the binding energy per nucleon**:
The binding energy per nucleon \( B \) is given by:
\[ B = \frac{E}{A} \]
Substitute the values:
\[ B = \frac{28.24 \, \text{MeV}}{4} = 7.06 \, \text{MeV} \]

6. **Final result**:
The binding energy per nucleon for helium is approximately \( 7.06 \, \text{MeV} \).