The mass equivalent of `931 MeV` energy is.

Options

A. `1.66 xx 10^-27 kg`
B. `6.02 xx 10^-24 kg`
C. `1.66 xx 10^-20 kg`
D. `6.02 xx 10^-27 kg`

Explanation

To find the mass equivalent of 931 MeV energy, we can use Einstein's mass-energy equivalence formula, which is given by:

\[ E = mc^2 \]

Where:
- \( E \) is the energy in joules,
- \( m \) is the mass in kilograms,
- \( c \) is the speed of light in a vacuum, approximately \( 3 \times 10^8 \, \text{m/s} \).

### Step-by-Step Solution:

1. **Convert Energy from MeV to Joules**:
The energy given is in MeV (mega electron volts). We need to convert this to joules. The conversion factor is:
\[ 1 \, \text{MeV} = 1.6 \times 10^{-13} \, \text{J} \]
Therefore, for 931 MeV:
\[ E = 931 \, \text{MeV} \times 1.6 \times 10^{-13} \, \text{J/MeV} = 1.4896 \times 10^{-10} \, \text{J} \]

2. **Use the Mass-Energy Equivalence Formula**:
Rearranging the formula \( E = mc^2 \) to solve for \( m \):
\[ m = \frac{E}{c^2} \]

3. **Substituting the Values**:
Now substitute the values of \( E \) and \( c \):
\[ m = \frac{1.4896 \times 10^{-10} \, \text{J}}{(3 \times 10^8 \, \text{m/s})^2} \]

4. **Calculating \( c^2 \)**:
First, calculate \( c^2 \):
\[ c^2 = (3 \times 10^8)^2 = 9 \times 10^{16} \, \text{m}^2/\text{s}^2 \]

5. **Calculating Mass \( m \)**:
Now substitute \( c^2 \) back into the equation for \( m \):
\[ m = \frac{1.4896 \times 10^{-10}}{9 \times 10^{16}} \]
\[ m = 1.6551 \times 10^{-27} \, \text{kg} \]

6. **Final Result**:
The mass equivalent of 931 MeV energy is approximately:
\[ m \approx 1.67 \times 10^{-27} \, \text{kg} \]

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