In a nuclear fission 0.1% of mass is converted into energy. The energy released by the fission of 1kg mass is

Options

A. `2.5xx10^7` KWH
B. `2.5xx10^7` J
C. `2.5xx10^7` eV
D. `2.5xx10^7` MeV

Answer

To solve the problem of calculating the energy released by the fission of 1 kg of mass when 0.1% of it is converted into energy, we can follow these steps:

### Step-by-Step Solution:

1. **Determine the mass converted into energy**:
Given that 0.1% of the mass is converted into energy, we first calculate the mass that is converted from 1 kg.
\[ \text{Mass converted} = 0.1\% \text{ of } 1 \text{ kg} = \frac{0.1}{100} \times 1 \text{ kg} = 0.001 \text{ kg} \]

2. **Use Einstein's mass-energy equivalence**:
According to Einstein's equation \(E = mc^2\), where \(E\) is the energy, \(m\) is the mass converted, and \(c\) is the speed of light (\(c = 3 \times 10^8 \text{ m/s}\)).
\[ E = 0.001 \text{ kg} \times (3 \times 10^8 \text{ m/s})^2 \]

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

4. **Calculate the energy**:
Now substitute \(c^2\) back into the equation for \(E\):
\[ E = 0.001 \text{ kg} \times 9 \times 10^{16} \text{ m}^2/\text{s}^2 = 9 \times 10^{13} \text{ J} \]

5. **Convert energy to kilowatt-hours (kWh)**:
To convert joules to kilowatt-hours, we use the conversion factor \(1 \text{ kWh} = 3.6 \times 10^6 \text{ J}\):
\[ E = \frac{9 \times 10^{13} \text{ J}}{3.6 \times 10^6 \text{ J/kWh}} \approx 2.5 \times 10^7 \text{ kWh} \]

### Final Answer:
The energy released by the fission of 1 kg mass is approximately \(2.5 \times 10^7 \text{ kWh}\).