Question
$$_{92}{U^{235}}{ + _0}{n^1} \to $$ fission product + neutron $$ + 3.2 \times {10^{ - 11}}J.$$ The energy released, when $$1g$$ of $$_{92}{U^{235}}$$ finally undergoes fission, is
A.
$$12.75 \times {10^8}\,k\,J$$
B.
$$18.60 \times {10^9}k\,J$$
C.
$$8.21 \times {10^7}\,k\,J$$
D.
$$6.55 \times {10^6}k\,J$$
Answer :
$$8.21 \times {10^7}\,k\,J$$
Solution :
$$235\,g\,\,{\text{of}}\,\,U - 235\,\,{\text{contains}}$$ $${\text{6}}{\text{.023}} \times {\text{1}}{{\text{0}}^{23}}\,{\text{atoms}}$$
$$\eqalign{
& 1\,g\,U - 235 = \frac{{6.023 \times {{10}^{23}}}}{{235}}\,atoms \cr
& \therefore \,\,{\text{Energy released}} \cr
& = \frac{{3.2 \times {{10}^{ - 11}} \times 6.023 \times {{10}^{23}}}}{{235}}J \cr
& = 8.21 \times {10^{10}}J \cr
& = 8.21 \times {10^7}\,kJ \cr} $$