In nuclear fission , `0.1%` mass in converted into energy. The energy released in the fission of `1 Kg` mass is

Options

A. `2.5xx10^(5) KWH`
B. `2.5xx10^(7) KWH`
C. `2.5xx10^(9) KWH`
D. `2.5xx10^(-7) KWH`

Explanation

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

### Step-by-Step Solution:

1. **Identify the mass converted to energy**:
Given that 0.1% of the mass is converted into energy, we first need to calculate how much mass this is for 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 formula**:
According to Einstein's equation, the energy (E) released when a mass (m) is converted into energy is given by:
\[ E = mc^2 \]
where \(c\) is the speed of light in a vacuum, approximately \(3 \times 10^8 \text{ m/s}\).

3. **Calculate the energy released**:
Substitute the mass converted (0.001 kg) and the speed of light into the equation:
\[ E = 0.001 \text{ kg} \times (3 \times 10^8 \text{ m/s})^2 \]
\[ E = 0.001 \times 9 \times 10^{16} \text{ J} = 9 \times 10^{13} \text{ J} \]

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

5. **Final answer**:
The energy released in the fission of 1 kg mass is approximately \(2.5 \times 10^7 \text{ kWh}\).