What role does half-life play in the making of an atomic bomb?
Half-life relates to the decay rate of the fissionables. When you multiply by the fraction of decays which are spontaneous fissions (instead of e.g. alpha emissions), you get the rate of events which can start a chain reaction. Why’s this important? A bomb needs to put together a supercritical mass before the chain reaction starts; once it has been blown apart far enough to be subcritical again, the chain reaction is over for all intents and purposes. The amount of time between going just barely critical and the design state of the bomb is problematic, because a premature start to the chain reaction can stop the process before it’s done (usually the explosive-driven collapse of a hollow sphere). If the half-life is really short or the bomb material has contaminants with short half-lives (and a spontaneous fission decay mode), you might have only a microsecond to go from the original sphere to the collapsed state without having the chain reaction start too soon. Plutonium-based bombs ha
