Question

The energy released by a bomb is sometimes expressed in tons of TNT (trinitrotoluene). When one ton of TNT explodes, $\mathbf{4}\mathbf{\times }{\mathbf{10}}^9\mathbf{J}$of energy is released. The fission of 1 mol of uranium releases approximately $\mathbf{2}\mathbf{\times }{\mathbf{10}}^{13}\mathbf{J}$J ofenergy. Calculate the energy released by the fission of 1.2 kg of uranium in a small atomic bomb. Express your answer in tons of TNT.

Short answer

Amount of energy released when 1.2 kg of uranium undergoes fission is$2.55\times {10}^4\text{\hspace{0.17em}ton\hspace{0.17em}of\hspace{0.17em}TNT}$ .

Step-by-step solution

Number of moles present in 1.2 kg of uranium

Atomic mass of uranium =235 g/mol

Number of moles present in 1.2 kg$=\frac{1.2\times {10}^3\mathrm{g}}{235\mathrm{g}/\mathrm{mol}}=5.10\mathrm{mol}$

Energy released in the fission reaction

Amount of energy released when 1 mol of uranium undergoes fission${\text{=2×10}}^{\text{13}}\text{\hspace{0.17em}J}$

Amount of energy released when 5.10 mol of uranium undergoes fission${\text{=2×10}}^{\text{13}}\times 5.10\text{\hspace{0.17em}J=10.2}\times {\text{10}}^{13}J$

Unit conversion

$\begin{array}{c}4\times {10}^9\mathrm{J}=1\mathrm{ton}\mathrm{of}\mathrm{TNT}\\ 10.2\times {10}^{13}\mathrm{J}=\frac{10.2\times {10}^{13}\mathrm{J}}{4\times {10}^9\mathrm{J}}\mathrm{ton}\mathrm{of}\mathrm{TNT}\\ =2.55\times {10}^4\text{}\mathrm{ton}\mathrm{of}\mathrm{TNT}\end{array}$

Therefore, amount of energy released when 1.2 kg of uranium undergoes fission is $2.55\times {10}^4\text{\hspace{0.17em}ton\hspace{0.17em}of\hspace{0.17em}TNT}$.