Q. The mass defect in particular nuclear reaction if 0.3 g. The amount of energy liberated in kilowatt hour is (Velocity of light$= \ 3\ \times \ 10^{8}\ ms^{- 1}$)
A) $1.5\ \times \ 10^{6}$
B) $2.5\ \times \ 10^{6}$
C) $3\ \times \ 10^{6}$
D) $7.5 \times \ 10^{6}$
Explanation
(d) $\ \ \ \ \ \ \ \ \ \ \mathrm{\Delta}m = 0.3g$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 0.3\ \times \ 10^{- 3}\ kg\ = \ 3\ \times \ 10^{- 4}\ kg$
Energy liberated , $E = \mathrm{\Delta}mc^{2}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 3\ \times \ 10^{- 4}\ \times \ \left( 3\ \times \ 10^{8} \right)^{2}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 3\ \times \ 10^{- 4}\ \times 9\ \times 10^{16}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \ 27\ \times 10^{12}\ \ J\ = \ \frac{27\ \times \ 10^{12}}{3.6\ \times \ 10^{6}}\ kWh$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \ 7.5\ \times \ 10^{6}\ \ kWh$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.