Question

An atom bomb is weighing 1 kg explodes releasing $9\times {10}^{13}$ joule of energy. What percentage of mass is converted into energy?

Answer 1

$E=m{c}^2$

$\Rightarrow 9\times {10}^{13}=m\times {(3\times {10}^8)}^2$

$9\times {10}^{13}=m\times 9\times {10}^{16}$

$m=\frac{9\times {10}^{13}}{9\times {10}^{16}}={10}^{-3}=-.001kg$

$\Rightarrow \%mass=\frac{0.001kg}{1kg}\times 100=0.1\%.$

Hence, the answer is $0.1\%.$