= Radioactive activity
{title2=$A=\lambda N$}
With $n$ parent <atomic nuclei> present, the conditional expected number of transformations in a short interval is approximately $\lambda n\Delta t$. The corresponding <radioactive activity> is $A=\lambda n$. Averaging over the <finite-population radioactive decay> model gives $\overline A(t)=\lambda\overline N(t)$. Its unit is the <becquerel>.<University Physics Volume 3 by Samuel J. Ling and others/10.3 Radioactive Decay>[University Physics Volume 3 by Samuel J. Ling and others; Equations 10.17–10.20 and the following becquerel definition]{ref}
For a finite counting interval, depletion matters. Suppose each transformation is recorded independently with <detection efficiency> $\varepsilon$, with at most one count per transformation and no background. The <expected value> of the count between $t$ and $t+\Delta t$ is
$$
\mathbb E[C]=\varepsilon\overline N(t)(1-e^{-\lambda\Delta t}).
$$
Only when $\lambda\Delta t\ll1$ does this become approximately $\varepsilon\overline A(t)\Delta t$. A count rate therefore needs a detector model before it can be interpreted as the source's <radioactive activity>.
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