A Decay Chain: the Daughter Is Radioactive Too

A parent decays to a radioactive daughter, which decays to a stable end product. Both activities are drawn against time on one shared vertical scale, which is honest here because the daughter's activity can never climb above the parent's starting activity. The daughter's peak is exactly where the two activities are equal, which is why the curves cross there. The sliders step in whole days and tenths of a day, so these are round-number chains that behave like the real ones — the calculator is where real half-lives go. The 100× line between secular and transient equilibrium is a stated convention, not a physical boundary; the limiting ratio beside it is the quantity that matters.

Decay constant, parent0.034657 per day
Decay constant, daughter0.346574 per day
Parent atoms left50.00 %
Daughter atoms5.54 %
Stable atoms44.46 %
Time now20.00 d
Daughter peaks at7.38 d
Limiting ratio1.1111

Both togetherTotal activity now 527.2 MBq. The dashed marker at 7.38 d is where the daughter activity peaks, and the two curves cross there because the peak is exactly where the two activities are equal.

The three percentages are each rounded on their own and are not presented as a sum. The ratio, the limiting ratio and the peak time do not depend on the source strength at all — it cancels — so the activity slider only sets the vertical scale.
Parent activity  A1 = λ1N1
250.0 MBq
Daughter activity  A2 = λ2N2
277.2 MBq
Activity ratio  A2/A1
1.1089
Which regime
Transient equilibrium
Parent half-life · T120 d
Daughter half-life · T22.0 d
Parent activity at the start500 MBq
Time, in parent half-lives1.00 T1
Time is set in multiples of the parent half-life so the graph stays readable at every T1; the same instant in days is in Time now. In secular equilibrium the chain settles onto a constant ratio just above 1 — it never reaches equality. Half-lives here are round numbers, not the real nuclides.