A small atomic bomb releases energy equivalent to the detonation of 20,000 tons of TNT; a ton of TNT releases \(4 \times 10^{9} \mathrm{~J}\) of energy when exploded. Using \(2 \times 10^{13} \mathrm{~J} / \mathrm{mol}\) as the energy released by fission of \({ }^{235} \mathrm{U}\), approximately what mass of \({ }^{235} \mathrm{U}\) undergoes fission in this atomic bomb?

The mass of \({ }^{235} \mathrm{U}\) undergoing fission in the atomic bomb can be calculated stepwise: Firstly, we calculate the total energy released by the explosion of 20,000 tons of TNT: Total energy released = \(4 \times 10^{9} \ \mathrm{J/ton} \) * (20,000 tons). Next, we compute the number of moles of \({ }^{235} \mathrm{U}\) required to release the calculated energy by dividing the total energy released by the energy released per mole of \({ }^{235} \mathrm{U}\) (\(2 \times 10^{13} \ \mathrm{J/mol}\)). Finally, we convert the number of moles to mass using the molar mass of \({ }^{235} \mathrm{U}\) (235 g/mol): Mass of \({ }^{235} \mathrm{U}\) = (Number of moles) * (Molar mass of \({ }^{235} \mathrm{U}\)).