If in nuclear fission, a piece of uranium of mass 0.5g is lost, the energy obtained (in kWh) is `n xx 10^(7)`. Find the value of n.

Explanation

To solve the problem, we need to calculate the energy obtained from the nuclear fission when 0.5 grams of uranium is lost. We will use the mass-energy equivalence principle given by Einstein's equation \(E = \Delta m c^2\).

### Step-by-Step Solution:

1. **Convert mass from grams to kilograms**:
\[ \Delta m = 0.5 \text{ g} = 0.5 \times 10^{-3} \text{ kg} \]

**Hint**: Remember that 1 kg = 1000 g, so to convert grams to kilograms, divide by 1000.

2. **Use the mass-energy equivalence formula**:
\[ E = \Delta m c^2 \]
where \(c\) (the speed of light) is approximately \(3 \times 10^8 \text{ m/s}\).

3. **Substitute the values into the equation**:
\[ E = (0.5 \times 10^{-3} \text{ kg}) \times (3 \times 10^8 \text{ m/s})^2 \]

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

5. **Calculate the energy**:
\[ E = 0.5 \times 10^{-3} \times 9 \times 10^{16} = 4.5 \times 10^{13} \text{ joules} \]

**Hint**: Ensure to multiply the coefficients and add the exponents correctly when using scientific notation.

6. **Convert energy from joules to kilowatt-hours**:
We know that \(1 \text{ kWh} = 3.6 \times 10^6 \text{ joules}\). Therefore, to convert joules to kilowatt-hours:
\[ E_{\text{kWh}} = \frac{E_{\text{joules}}}{3.6 \times 10^6} \]
\[ E_{\text{kWh}} = \frac{4.5 \times 10^{13}}{3.6 \times 10^6} \]

7. **Perform the division**:
\[ E_{\text{kWh}} = 1.25 \times 10^{7} \text{ kWh} \]

8. **Identify the value of \(n\)**:
The energy can be expressed as \(n \times 10^7\) kWh, where \(n = 1.25\).

### Final Answer:
The value of \(n\) is \(1.25\).