When U-235 undergoes fission, 0.1% of its mass is converted into energy. Then amount of energy released during the fission of 1kg of uranium-235 will be

Options

A. `9xx10^13` J
B. `9xx10^14` J
C. `9xx10^15` J
D. `9xx10^21` J

Answer

To find the amount of energy released during the fission of 1 kg of uranium-235 (U-235), we can follow these steps:

### Step 1: Determine the mass converted to energy
When U-235 undergoes fission, 0.1% of its mass is converted into energy.

\[ \text{Mass converted} = 0.1\% \text{ of } 1 \text{ kg} = \frac{0.1}{100} \times 1 \text{ kg} = 0.001 \text{ kg} = 10^{-3} \text{ kg} \]

### Step 2: Use Einstein's equation to calculate energy
According to Einstein's mass-energy equivalence principle, the energy (E) released can be calculated using the formula:

\[ E = m \cdot c^2 \]

Where:
- \( m \) is the mass converted to energy (which we found to be \( 10^{-3} \text{ kg} \)),
- \( c \) is the speed of light, approximately \( 3 \times 10^8 \text{ m/s} \).

### Step 3: Substitute the values into the equation
Now we can substitute the values into the equation:

\[ E = 10^{-3} \text{ kg} \cdot (3 \times 10^8 \text{ m/s})^2 \]

Calculating \( (3 \times 10^8)^2 \):

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

### Step 4: Calculate the energy
Now substituting back into the energy equation:

\[ E = 10^{-3} \cdot 9 \times 10^{16} = 9 \times 10^{13} \text{ joules} \]

### Conclusion
The amount of energy released during the fission of 1 kg of uranium-235 is:

\[ \boxed{9 \times 10^{13} \text{ joules}} \]