The mass defect in a particular nuclear reaction is 0.3 g. The amount of energy liberated in kilowatt-hour (kWh) is-
(Velocity of light = 3 × 108 m/s)
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 7.5 × 106
The mass defect is converted into energy by Einstein’s mass-energy relation; the energy in joules is then converted into kilowatt-hours.
\( \Delta m = 0.3\,\mathrm{g} = 3\times10^{-4}\,\mathrm{kg} \)
\( E = \Delta m\,c^{2} \)
\( E = 3\times10^{-4}\,\mathrm{kg} \times (3\times10^{8}\,\mathrm{m\,s^{-1}})^{2} \)
\( E = 2.7\times10^{13}\,\mathrm{J} \)
\( 1\,\mathrm{kWh} = 1000\,\mathrm{W} \times 3600\,\mathrm{s} = 3.6\times10^{6}\,\mathrm{J} \)
\( \displaystyle E = \frac{2.7\times10^{13}\,\mathrm{J}}{3.6\times10^{6}\,\mathrm{J\,kWh^{-1}}} \)
\( E = 7.5\times10^{6}\,\mathrm{kWh} \)