Question

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

Short answer

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

Step-by-step solution

Number of moles present in 1.2 kg of uranium

Atomic mass of uranium $=235\mathrm{g}$

Number of moles present in$1.2\mathrm{kg}$$=\frac{1.2\times {10}^3\mathrm{g}}{235\mathrm{g}{\mathrm{mol}}^{-1}}=5.10\mathrm{mol}$

Energy released in the fission reaction

Amount of energy released when 1 mol of uranium undergoes fission$=2\times {10}^{13}\mathrm{J}$

Amount of energy released when $5.10\mathrm{mol}$of uranium undergoes fission$=5.10\times 2\times {10}^{13}\mathrm{J}=10.2\times {10}^{13}\mathrm{J}$

Unit conversion

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

Therefore, amount of energy released when $1.2\mathrm{kg}$of uranium undergoes fission is$2.55\times {10}^4$ tons of TNT.