If in a nuclear fission, piece of uranium of mass `0.5 g` is lost, the energy obtained in `kWh` is.

Options

A. `1.25 xx 10^7`
B. `2.25 xx 10^7`
C. `3.25 xx 10^7`
D. `0.25 xx 10^7`

Explanation

To solve the problem of finding the energy obtained from the loss of a 0.5 g piece of uranium during nuclear fission, we can follow these steps:

### Step-by-Step Solution:

1. **Convert mass from grams to kilograms**:
\[ \text{Mass} = 0.5 \, \text{g} = 0.5 \times 10^{-3} \, \text{kg} = 5 \times 10^{-4} \, \text{kg} \]

2. **Use the mass-energy equivalence formula**:
The energy (E) released can be calculated using Einstein's mass-energy equivalence formula:
\[ E = \Delta m \cdot c^2 \]
where \( c \) (the speed of light) is approximately \( 3 \times 10^8 \, \text{m/s} \).

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

4. **Substitute the values into the equation**:
\[ E = (5 \times 10^{-4} \, \text{kg}) \cdot (9 \times 10^{16} \, \text{m}^2/\text{s}^2) \]
\[ E = 4.5 \times 10^{13} \, \text{J} \]

5. **Convert energy from joules to kilowatt-hours**:
To convert joules to kilowatt-hours, we use the conversion factor:
\[ 1 \, \text{kWh} = 3.6 \times 10^6 \, \text{J} \]
Therefore, to convert joules to kilowatt-hours:
\[ E \, (\text{kWh}) = \frac{E \, (\text{J})}{3.6 \times 10^6} \]
\[ E \, (\text{kWh}) = \frac{4.5 \times 10^{13}}{3.6 \times 10^6} \]

6. **Calculate the final value**:
\[ E \, (\text{kWh}) = 1.25 \times 10^7 \, \text{kWh} \]

### Final Answer:
The energy obtained from the loss of 0.5 g of uranium in nuclear fission is:
\[ \boxed{1.25 \times 10^7 \, \text{kWh}} \]

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