Question

If $200MeV$ of energy is released in the fission of one nucleus of ${}_{92}^{236}U$, the number of nuclei that must undergo fission to release an energy of $1000J$ is:

• A. $3.125\times {10}^{13}$
• B. $6.25\times {10}^{13}$
• C. $12.5\times {10}^{13}$
• D. $3.125\times {10}^{14}$

Answer 1

Answer: (A)

$3.125\times {10}^{13}$

One ${}_{92}^{236}U$ nucleus gets split in one fission reaction.

Total energy released in $n$ such fission reactions: $E=1000J$

Energy released per fission reaction: $Q=200$ $MeV=200\times 1.6\times {10}^{-13}J=320\times {10}^{-13}J$

$\therefore$ Number of fission reactions (or ${}_{92}^{236}U$ nuclei involved):

$n=\frac{E}{Q}=\frac{1000}{320\times {10}^{-13}}=3.125\times {10}^{13}$ nuclei