Energy released as mass of `2 "amu"` is converted into energy is

Options

A. `1.5xx10^(-10)J`
B. `3xx10^(-10)J`
C. `1863 J`
D. `931.5 MeV`

Explanation

To find the energy released when a mass of 2 amu is converted into energy, we can use the famous equation from Einstein's theory of relativity:

### Step-by-Step Solution:

1. **Understand the relationship between mass and energy**:
The energy \( E \) released when a mass \( m \) is converted into energy is given by the equation:
\[ E = mc^2 \]
where \( c \) is the speed of light in a vacuum, approximately \( 3 \times 10^8 \) m/s.

2. **Convert atomic mass units (amu) to energy**:
We know that 1 amu corresponds to approximately 931.5 MeV (mega electron volts) of energy. Therefore, for 2 amu:
\[ E = 2 \, \text{amu} \times 931.5 \, \text{MeV/amu} = 1863 \, \text{MeV} \]

3. **Convert MeV to joules**:
To convert MeV to joules, we use the conversion factor:
\[ 1 \, \text{MeV} = 1.6 \times 10^{-13} \, \text{joules} \]
Thus, the energy in joules is:
\[ E = 1863 \, \text{MeV} \times 1.6 \times 10^{-13} \, \text{joules/MeV} \]

4. **Calculate the energy in joules**:
Performing the multiplication:
\[ E = 1863 \times 1.6 \times 10^{-13} = 2980.8 \times 10^{-13} \, \text{joules} \]
This can be rounded to:
\[ E \approx 2.98 \times 10^{-10} \, \text{joules} \]

5. **Conclusion**:
Therefore, the energy released when a mass of 2 amu is converted into energy is approximately:
\[ E \approx 2.98 \times 10^{-10} \, \text{joules} \]