3. The yield of an atomic bomb Little Boy was the codename of the atomic bomb which was dropped on Hiroshima, on August 6. 1945 by the B-29 Enola Gay. It was the first atomic bomb ever used as a weapon and was dropped three days before the plutonium powered "Fat Man" bomb was used against Nagasaki. It is estimated that up to 140,000 people were killed as a result of the Hiroshima bomb. Little Boy used a gun-type mechanism to achieve critical fission mass whereby a "bullet of 235U was fired into a 23 target to produce a supercritical mass of uranium (large enough to initiate a nuclear chain reaction). In all, Little Boy contained 64 kg of 233U of which about 0.82 kg underwent nuclear fission. Estimate the amount of energy released during fission from the following steps: a. Calculate the number of atoms of 2SU that underwent fission. b. For each of the three reactions given below calculate the mass defect by summing the mass of each side and then use Einstein's equation to calculate the energy that this mass defect equates to (in MeV): 235U + n4Ba + "Kr + 2n + energy 235U + 1 + 141Ba + 9Kr + 3n+ energy 235U + 1 92Sr + Xe + 4n+ energy Use the following atomic masses Neutronn 90Kr 9 Kr Mass (amu) 1.00866 89.919525 91.926155 91.911034 92S1 140Xe 14 Ba 14Ba 139.921631 140.914413 143.922943 1330 235.043923 c. Assume that the explosion involves just the above reactions and that the three reactions occur with equal frequency. Calculate the total energy released by 0.82 kg of 23SU. Give your answer in both joules (J) and kilotons (the amount of energy produced by 1 ton of TNT, equal to 4.2 x 1012 ). Look on the internet to find the reported yield of the Little Boy bomb - how does your calculated explosive yield compare? d. Combustion of one ton of coal (i.e. 1000 kg) is equivalent to about 29.3 x 10 J. How much more energy does the fission of 2s produce compared to coal on an equal weight basis (1.e. per kg of coal or 235U)