Question

A nuclear explosive is designed to deliver $1\, MW$ 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 $200\, MeV$ )

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

Answer 1

Answer: (D)

Energy released per fission is
$E =200\, MeV$
$=200 \times 1.6 \times 10^{-13}$
$=3.2 \times 10^{-11} J$
Total energy required to run a $1\, MW$ reactor for one year is
$=10^{6} Js ^{-1} \times(365 \times 24 \times 60 \times 60)$
$=3.15 \times 10^{13} J$
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 $235 g$ of $U ^{235}$
$\therefore $ Mass of $U ^{235}$ containing $9.84 \times 10^{23}$ atoms is
$M=\frac{235}{6.02 \times 10^{23}} \times 9.84 \times 10^{23}$
$=384\, g =0.384\, kg$