E.3.20 (HL)—Decay constant meaning

Define lambda

The decay constant $\lambda$ is the probability per unit time that an individual undecayed nucleus will decay, in the small-time interval sense. Its unit is inverse time.

Use the approximation

When $\lambda\Delta t$ is very small, $\lambda\Delta t$ approximates the probability that a particular nucleus decays during $\Delta t$. The exact exponential law applies over longer intervals.

Separate lambda from activity

$\lambda$ describes a property of the nuclide. Activity $A$ describes the whole sample and depends on how many nuclei remain: $A=\lambda N$.

Common trap

Do not call lambda the number of decays per second of the whole sample; that is activity.