Question

The mass of ${}_{92}^{235}\text{U}$ which must go nuclear fission to produce the same mass of energy as produced by 1 ton of coal. Given the heat of combustion of coal is $8\times {10}^{3}cal/g$. The fission of ${}_{92}^{235}\text{U}$ produces 200 MeV energy per fission. $($Use $1cal=4.2J;1ton={10}^{6}g)$.

• A. 0.5165 g
• B. 0.2345 g
• C. 0.8185 g
• D. 0.4145 g

Answer 1

The correct option is D 0.4145 g

The energy produced by the combustion of 1 ton of coal is

${10}^{6}g\times 8\times {10}^{3}cal/g=8\times {10}^{9}cal$

Convert the unit in J

$8\times {10}^{9}cal\times \frac{4.2J}{1cal}=3.36\times {10}^{10}J$

Convert the unit into MeV.

$3.36\times {10}^{10}J\times \frac{1MeV}{1.60\times {10}^{-13}J}=2.1\times {10}^{23}MeV$

The fission of one U atom produces 200 MeV energy.

Thus $2.1\times {10}^{23}MeV$ energy corresponds to $\frac{2.1\times {10}^{23}MeV}{200}=1.05\times {10}^{21}$ nuclei of U.

The mass of U is $\frac{1.05\times {10}^{21}}{6.023\times {10}^{23}}\times 235=0.4145g$