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.
Mass equivalent to the energy `931 MeV` is

Options

A. `6.02 xx 10^(-27) kg`
B. `1.662 xx 10^(-27) kg`
C. `16.66 xx 10^(-27) kg`
D. `16.02 xx 10^(-27) kg`

Answer

To solve the problem regarding the mass equivalent to the energy of 931 MeV, we will follow these steps:

### Step 1: Understand the relationship between energy and mass
The energy-mass equivalence is given by Einstein's equation:
\[ E = \Delta m c^2 \]
Where:
- \( E \) is the energy in joules,
- \( \Delta m \) is the mass defect in kilograms,
- \( c \) is the speed of light, approximately \( 3 \times 10^8 \) m/s.

### Step 2: Convert energy from MeV to joules
We need to convert the energy given in MeV to joules. The conversion factor is:
\[ 1 \text{ MeV} = 1.6 \times 10^{-13} \text{ joules} \]
Thus, for 931 MeV:
\[ E = 931 \text{ MeV} \times 1.6 \times 10^{-13} \text{ joules/MeV} = 1.4896 \times 10^{-10} \text{ joules} \]

### Step 3: Rearrange the equation to find mass
From the equation \( E = \Delta m c^2 \), we can rearrange it to solve for \( \Delta m \):
\[ \Delta m = \frac{E}{c^2} \]

### Step 4: Substitute the values into the equation
Now we can substitute the values we have:
- \( E = 1.4896 \times 10^{-10} \text{ joules} \)
- \( c = 3 \times 10^8 \text{ m/s} \)

Calculating \( c^2 \):
\[ c^2 = (3 \times 10^8)^2 = 9 \times 10^{16} \text{ m}^2/\text{s}^2 \]

Now substituting into the mass equation:
\[ \Delta m = \frac{1.4896 \times 10^{-10}}{9 \times 10^{16}} \approx 1.655 \times 10^{-27} \text{ kg} \]

### Step 5: Round the result
Rounding off the result gives:
\[ \Delta m \approx 1.67 \times 10^{-27} \text{ kg} \]

### Conclusion
The mass equivalent to the energy of 931 MeV is approximately \( 1.67 \times 10^{-27} \text{ kg} \).

### Final Answer
The answer is option **B**: \( 1.67 \times 10^{-27} \text{ kg} \).

---