Question

2. 23 U is a fissile isotope of uranium, used in the atomic bomb dropped on Hiroshima in 1945. The critical mass is 56 kg. The primary isotope is not fissile and had to be removed by a process which required synthesis of UFs, a gas. How much 235UF was required to produce a critical mass of the element? [Molar masses: U, 235.0439 g; F, 18.9984 g)

Answer 1

Mass of U-235 needed = 56 kg = 56000 g

Molar Mass of U-235 = 235.0439 g/mol

Moles of U-235 needed = Mass/ Molar Mass = 56000 g / (235.0439 g/mol)=238.253 mol

1 mole of UF₆ give 1 mole U-235. Thus moles of UF₆ needed = 238.253 mol

Molar Mass of UF₆ = 235.0439 + 6 * 18.9984 g/mol = 349.0343 g/mol

Thus, weight of UF₆ needed = Moles * Molar Mass = 238.253 mol * 349.0343 g/mol = 83158.47 g = 83.158 kg

Thus, the amount of UF₆ needed is 83.158 kg.