Question

In a nuclear reactor, the fuel is consumed at the rate of \( 1 \times 10^{-3} \) gs\(^{-1}\). The power generated in kW is:

• A. \( 9 \times 10^{14} \)
• B. \( 9 \times 10^{7} \)
• C. \( 9 \times 10^{8} \)
• D. \( 9 \times 10^{12} \)

Hint:

Nuclear reactions release energy based on mass conversion using Einstein’s equation \( E = mc^2 \).

Answer 1

The Correct Option is B

Step 1: Use Energy
-Mass Relation Using Einstein’s mass-energy equivalence: \[ E = mc^2 \] where: - \( m = 1 \times 10^{-3} \) g = \( 1 \times 10^{-6} \) kg, - \( c = 3 \times 10^8 \) m/s. 
Step 2: Compute Power Energy released per second: \[ P = (1 \times 10^{-6}) \times (9 \times 10^{16}) \] \[ P = 9 \times 10^{10} \text{ W} = 9 \times 10^7 \text{ kW} \]