Q. An atomic power nuclear reactor can deliver 300 MW. The energy released due to fission of each nucleus of uranium atom $U^{238}$ is 170 MeV. The number of uranium atoms fissioned per hour will be
A) $30\ \times \ 10^{25}$
B) $4 \times \ 10^{22}$
C) $10\ \times \ 10^{20}$
D) $5 \times \ 10^{15}$
Explanation
(b) Power = $\frac{energy}{time}$ $= \ 300\ \times \ 10^{6}\ \ watt$
$\ \ \ = \ 3\ \times \ 10^{8}\ J/s$
$170\ MeV\ = \ 170\ \times \ 10^{6} \times 1.6\ \times \ 10^{- 19}$
$= 27.2\ \times \ 10^{- 12}\ J$
Number of atoms fissioned per second
= $\frac{3\ \times 10^{8}}{27.2\ \times 10^{- 12}}$
= $\frac{3 \times 10^{20}}{27.2}$
Number of atoms fissioned per hour
= $\frac{3\ \times 10^{20} \times \ 3600}{27.2\ }$
= $\frac{3 \times 36}{27.2} \times 10^{22}\ = \ 4\ \times \ 10^{22}\ m$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.