Question

In a nuclear fission. $0.1\%$ mass is converted into energy. The energy released by the fission of $1\, kg$ mass will be:

• A. $ 9\times {{10}^{19}}\, J $
• B. $ 9\times {{10}^{17}}\, J $
• C. $ 9\times {{10}^{16}}\, J $
• D. $ 9\times {{10}^{13}}\, J $

Answer 1

Answer: (D)

Mass can be converted into energy using mass-energy equivalence.
If a substance loses an amount $\Delta m$ of its mass, an equivalent amount $\Delta E$ of energy is produced, where
$\Delta E=(\Delta m) c^{2}$
Where $c$ is speed of light.
This is called Einstein's mass energy relation.
Amount of mass converted into energy is,
$\Delta m=\frac{0.1}{100} \times 1=10^{-3}\, kg $
and $ c=3 \times 10^{8} \,m / s $
$\therefore \Delta E=10^{-3} \times\left(3 \times 10^{8}\right)^{2}$
$\Delta E=9 \times 10^{13} J$