Question

The energy released when one nucleus of ${ }_{92} U ^{235}$ undergoes fission is $188 \,MeV$. The energy released when $100\, g$ of ${ }_{92} U ^{235}$ undergoes fission is

• A. $3.55 \times 10^{12} \,J$
• B. $7.71 \times 10^{12}\,J$
• C. $3.55 \times 10^{13}\, J$
• D. $7.71 \times 10^{13}\, J$

Answer 1

Answer: (B)

Given, energy released, $E_{0}=188\, MeV$ per nucleus fission and mass, $m=100\,gm$
As number of nucleus in $100\, gm$ of ${ }_{92} U ^{235}$
$N=\frac{100}{M} \times N_{A}$
where, $N_{A}=$ Avogadro number and
$M $ = molecular mass
$\Rightarrow \, N=\frac{100}{235} \times 6.022 \times 10^{23}=2 \cdot 56 \times 10^{23}$ nucleus
Energy released in fission of one nucleus
$E_{0}' =E_{0}=188 \times 10^{6} \times 1.6 \times 10^{-19} \,J $
$=300.8 \times 10^{-13}\, J$
So, Energy released in N-nucleus fission,
$ E=E_{0}' N=2 \cdot 5610^{23} \times 300.8 \times 10^{-13} \,J $
$\Rightarrow \, E=7.71 \times 10^{12} \,J$