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`

Explanation

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

### Step 1: Understand the relationship between mass and energy
In nuclear reactions, the energy released when a mass \( m \) is converted to energy can be calculated using Einstein's mass-energy equivalence formula:
\[ E = mc^2 \]
where \( c \) is the speed of light, approximately \( 3 \times 10^8 \) m/s.

### Step 2: Convert the mass consumption rate to kilograms
The fuel is consumed at a rate of \( 1 \) mg/s. To convert this to kilograms:
\[ 1 \text{ mg} = 1 \times 10^{-3} \text{ g} = 1 \times 10^{-6} \text{ kg} \]
Thus, the mass consumption rate is:
\[ \frac{m}{t} = 1 \times 10^{-6} \text{ kg/s} \]

### Step 3: Calculate the energy generated per second
Using the mass-energy equivalence, the energy generated per second (which is power) can be calculated as:
\[ P = \frac{E}{t} = \frac{m}{t} c^2 \]
Substituting the values:
\[ P = (1 \times 10^{-6} \text{ kg/s}) \times (3 \times 10^8 \text{ m/s})^2 \]

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

### Step 5: Substitute \( c^2 \) into the power equation
Now substituting \( c^2 \) back into the power equation:
\[ P = (1 \times 10^{-6}) \times (9 \times 10^{16}) = 9 \times 10^{10} \text{ watts} \]

### Step 6: Convert watts to kilowatts
To convert watts to kilowatts, we divide by \( 1000 \):
\[ P = \frac{9 \times 10^{10}}{1000} = 9 \times 10^{7} \text{ kilowatts} \]

### Final Answer
The power generated in the nuclear reactor is:
\[ \boxed{9 \times 10^{7} \text{ kilowatts}} \]

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