Question

The mass defect in a particular nuclear reaction is \(0.3 \, \text{g}\). The amount of energy liberated in kilowatt-hours is (velocity of light \( = 3 \times 10^8 \, \text{m/s}\)).

• A. $1.5\times 10^{6}$
• B. $2.5\times 10^{6}$
• C. $3\times 10^{6}$
• D. $7.5\times 10^{6}$

Hint:

$E = \Delta m c^2$, and $1$ kWh = $3.6 \times 10^6$ J.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
$E = \Delta m c^2$, and $1$ kWh = $3.6 \times 10^6$ J.
Step 2: Detailed Explanation:
$E = \Delta m c^2 = (0.3 \times 10^{-3}) \times (3 \times 10^8)^2 = 0.3 \times 10^{-3} \times 9 \times 10^{16} = 2.7 \times 10^{13}$ J. $1$ kWh = $3.6 \times 10^6$ J. So $E = \frac{2.7 \times 10^{13}}{3.6 \times 10^6} = 7.5 \times 10^6$ kWh.
Step 3: Final Answer:
The energy liberated is $7.5 \times 10^6$ kWh.