| MadSci Network: Physics |
The yield from the Hiroshima bomb has been estimated at 6 * 10^13 joule. The value of c is close to 3 * 10^8 m/sec. The amount of mass converted must therefore be
6 * 10^13 = m * (3 * 10^8) ^2
giving m = 0.67 * 10^-3 kg, or 0.67 gram.
The molar mass of U-235 is given as 235.0439 g/mol.
A possible fission pathway might be to Ba-140 and Kr-92 and 3 neutrons. In the course of subsequent decay, the Ba-140 would become Ce-140, with molar mass 139.9053, and the Kr-92 would become Zr-92, with molar mass 91.9046. The molar mass of each neutron is 1.00867.
The overall equation then has molar mass changing from 235.0439 to 234.8359, amounting to a loss of 0.208 gram per mole. If this equation, and the published yield are anywhere near right, there must have been just over 3 mole of U-235 (about 800 gram) transmuted into fission products. The particular fission products I have chosen are particularly low energy ones. Other pathways may yield less energy, and I have also included the energy of subsequent beta-decay in the yield, which the original estimate probably did not. So I suspect that in practice rather more than 1 kg of U-235 was transmuted.
But the result of 0.67 gram of matter lost is a firm one.
Try the links in the MadSci Library for more information on Physics.