Rule of thumb · PhysicsNº 71 / 238

The half-life is about seven-tenths of the mean life

How is the half-life related to the mean life of an atom?

The half-life is about 0.7 of the mean life; the mean life is about 1.44 half-lives.

Why it works

The mean life is 1/λ and the half-life ln 2/λ, so their ratio is ln 2 = 0.693. The average atom lasts longer than the half-life because the few that survive a long time pull the average up: after one mean life, 37% are still there, not half.

When it fails

The half-life describes the sample and the mean life describes the atom; confusing them makes lifetimes look 44% too short. The mean life says nothing about when a particular atom will go: because the decay is memoryless, an atom that has already survived a long time has exactly the same chance of going in the next second as a new one.

Do it exactly

Estimate with the rule, then check it against the calculator that models it properly.

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