Question

The mass defect in a particular nuclear reaction is $0.3\text{g}$. The amount of energy liberated in kilowatt-hour $\left(\text{kWh}\right)$ is
$(\text{Velocity of light,}c=3\times {10}^8{\text{ms}}^{-1})$

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

Answer 1

The correct option is D $7.5\times {10}^6$

Given:
The mass defect
$\Delta m=0.3\text{g}=0.3\times {10}^{-3}\text{kg}$

According to the Einstein's mass energy equivalence,

Energy liberated

$E=\left(\Delta m\right)c^2$

$\Rightarrow E=(0.3\times {10}^{-3})(3\times {10}^8{)}^2$

$\Rightarrow E=3\times {10}^{-4}\times 9\times {10}^{16}$

$\Rightarrow E=27\times {10}^{12}\text{J}$

We know that,

$1\text{kWh}=36\times {10}^5\text{J}$

$\Rightarrow E=\frac{27\times {10}^{12}}{36\times {10}^5}\text{kWh}$

$\Rightarrow E=\frac{3}{4}\times {10}^7\text{kWh}=0.75\times {10}^7\text{kWh}$

$\Rightarrow E=7.5\times {10}^6\text{kWh}$

Hence, option $\left(D\right)$ is correct.