Question

The energy in $\text{MeV}$ released due to conversion of $1\text{kg}$ mass completely into energy is $(c=3\times {10}^8{\text{ms}}^{-1})$

• A. $5.625\times {10}^{29}\text{MeV}$
• B. $29\times {10}^5\text{MeV}$
• C. $7.625\times {10}^9\text{MeV}$
• D. $2.8\times {10}^{15}\text{MeV}$

Answer 1

The correct option is A $5.625\times {10}^{29}\text{MeV}$

Given:
$m=1\text{kg}$ ; $c=3\times {10}^8{\text{ms}}^{-1}$

According to Einstein's mass-energy equivalence equation,

$E=m{c}^2$

$\Rightarrow E=1\times (3\times {10}^8{)}^2$

$\Rightarrow E=9\times {10}^{16}\text{J}$

We know that,

$1\text{MeV}=1.6\times {10}^{-13}\text{J}$

$\begin{array}{c}1\text{J}=\frac{1}{1.6\times {10}^{-13}}\text{MeV}\end{array}$

$\Rightarrow E=9\times {10}^{16}\times \frac{1}{1.6\times {10}^{-13}}$

$\Rightarrow E=5.625\times {10}^{29}\text{MeV}$

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