Question

A nuclear explosive is designed to deliver $1MW$ power in the form of heat energy. If the explosion is designed with nuclear fuel consisting of $U^{235}$ to run a reactor at this power level for one year, then the amount of fuel needed is (Given energy per fission is $200MeV$ )

• A. 1 kg
• B. 0.01 kg
• C. 3.84 kg
• D. 0.384 kg

Answer 1

Answer: (D)

Energy released per fission is
$E=200MeV$
$=200\times 1.6\times 10^{-13}$
$=3.2\times 10^{-11}J$
Total energy required to run a $1MW$ reactor for one year is
$=10^{6}J{s}^{-1}\times (365\times 24\times 60\times 60)$
$=3.15\times 10^{13}J$
Since, 1 fission ( 1 atom of $U^{235}$ ) produces $3\cdot 2\times 10^{-11}J$ of energy. S0, total number of $U^{235}$ atoms required is
$\frac{3.15\times 10^{13}}{3.2\times 10^{-11}}$
$=9.84\times 10^{23}$
Now, $6.02\times 10^{23}$ atoms of $U^{235}$ are contained in $235g$ of $U^{235}$
$\therefore$ Mass of $U^{235}$ containing $9.84\times 10^{23}$ atoms is
$M=\frac{235}{6.02\times 10^{23}}\times 9.84\times 10^{23}$
$=384g=0.384kg$