In a nuclear reactor, the fuel is consumed at the rate of `1 mg//s`. The power generated in kilowatt is.

Options

A. `9 xx 10^4`
B. `9 xx 10^7`
C. `9 xx 10^8`
D. `9 xx 10^(12)`

Answer

To solve the problem of calculating the power generated in a nuclear reactor where the fuel is consumed at a rate of 1 mg/s, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Data**:
- The rate of fuel consumption is given as \( \frac{m}{t} = 1 \, \text{mg/s} \).
- We need to convert this rate into kilograms for standard SI units.
- \( 1 \, \text{mg} = 1 \times 10^{-6} \, \text{kg} \).

2. **Convert the Fuel Consumption Rate**:
- Convert 1 mg/s to kg/s:
\[ \frac{m}{t} = 1 \, \text{mg/s} = 1 \times 10^{-6} \, \text{kg/s} \]

3. **Use the Energy-Mass Equivalence**:
- According to Einstein's equation, the energy \( E \) produced from mass \( m \) is given by:
\[ E = mc^2 \]
- Here, \( c \) (the speed of light) is approximately \( 3 \times 10^8 \, \text{m/s} \).

4. **Calculate the Energy Produced Per Second**:
- Since we are looking for power, which is energy per unit time, we can express power \( P \) as:
\[ P = \frac{E}{t} = \frac{mc^2}{t} \]
- Since \( \frac{m}{t} = 1 \times 10^{-6} \, \text{kg/s} \), we can substitute this into the equation:
\[ P = \left(1 \times 10^{-6} \, \text{kg/s}\right) \cdot (3 \times 10^8 \, \text{m/s})^2 \]

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

6. **Substitute and Calculate Power**:
- Now substitute \( c^2 \) back into the power equation:
\[ P = 1 \times 10^{-6} \cdot 9 \times 10^{16} = 9 \times 10^{10} \, \text{W} \]

7. **Convert Watts to Kilowatts**:
- Since \( 1 \, \text{kW} = 1000 \, \text{W} \), convert power to kilowatts:
\[ P = \frac{9 \times 10^{10}}{1000} = 9 \times 10^7 \, \text{kW} \]

8. **Final Answer**:
- The power generated in the nuclear reactor is:
\[ P = 9 \times 10^7 \, \text{kW} \]