E.3.21 (HL)—Activity equation

Use the activity relation

Activity is the decay rate: $A=\lambda N$. Combining this with the decay law gives $A=\lambda N_0e^{-\lambda t}$.

Worked example — number of nuclei

If $A=2.5\times10^5\,\mathrm{Bq}$ and $\lambda=1.8\times10^{-6}\,\mathrm{s^{-1}}$, then $N=A/\lambda=(2.5\times10^5)/(1.8\times10^{-6})=1.4\times10^{11}$ undecayed nuclei.

Find N first

For a sample mass $m$, find the number of nuclei using $N=(m/M)N_A$ before multiplying by $\lambda$. Use the isotopic molar mass and consistent units.

Track time dependence

Activity falls with the same exponential factor as the number of undecayed nuclei. If $t=0$, use $A_0=\lambda N_0$.

Common trap

Do not multiply lambda by sample mass directly. Convert mass to a number of nuclei first.