Question

One milligram of matter converted into energy will give

• A. $9$ J
• B. $9\times {10}^{13}$ J
• C. $9\times {10}^5$ J
• D. $9\times {10}^{10}$ J

Answer 1

Answer: (D)

$9\times {10}^{10}$ J

$\begin{array}{c}\text{Energy released by}1\text{amu}=931MeV\\ \begin{array}{cc}\mathrm{l\; amu}& =1.67\times {10}^{-27}kg\\ & =1.67\times {10}^{-24}gram\end{array}\end{array}$

$\begin{array}{c}\text{So,}1.67\times {10}^{-24}\text{gram release}=931MeV\\ \therefore \text{1 gram release}=\frac{931}{1.67\times {10}^{-24}}MeV\end{array}$

$\begin{array}{c}\text{1. milligram release}=\frac{931\times {10}^{-3}}{1.67\times {10}^{-24}}\times {10}^{6}eV\\ \therefore 1eV=1.6\times {10}^{-19}J\end{array}$

$=\frac{931\times {10}^{-3}\times {10}^6\times 1.6\times {10}^{-19}}{1.67\times {10}^{-24}}J$

$\begin{array}{cc}E& =891.9\times {10}^{8}J\\ E& =9\times {10}^{10}\text{joule}\end{array}$