Calculator Inputs
Example Data Table
| Stage | Nuclide | Half-life | Molar mass (g/mol) | Branch to next (%) | Example note |
|---|---|---|---|---|---|
| 1 | Parent A | 5 days | 226 | 100 | Initial amount entered by user |
| 2 | Daughter B | 2 days | 222 | 100 | Builds as Parent A decays |
| 3 | Daughter C | 12 hours | 218 | 100 | Intermediate decay product |
| 4 | Daughter D | 1 hour | 214 | 100 | Fast short-lived stage |
| 5 | Stable E | 0 | 210 | — | Accumulated stable end product |
Formula Used
This calculator models a linear decay chain where each nuclide feeds the next one. It converts half-lives to decay constants, solves the coupled differential equations, and reports amount, mass, and activity for every stage.
Decay constant:
λᵢ = ln(2) / T½,ᵢ
Parent stage:
dN₁/dt = -λ₁N₁
For every daughter stage:
dNᵢ/dt = bᵢ₋₁ λᵢ₋₁ Nᵢ₋₁ - λᵢNᵢ
Activity:
Aᵢ = λᵢNᵢ
Moles:
nᵢ = Nᵢ / Nₐ
Mass:
mᵢ = nᵢ × Mᵢ
Here, N is atoms, b is branch fraction, Nₐ is Avogadro’s constant, and M is molar mass. Numerical integration uses a fourth-order Runge–Kutta routine.
How to Use This Calculator
- Enter the initial parent amount and choose atoms, moles, or grams.
- Set the elapsed time and select the matching time unit.
- Choose how many stages you want to include in the chain.
- Fill each stage with a nuclide label, half-life, and molar mass.
- Enter branch fractions for transfers to the next stage when needed.
- Use a half-life of zero only for the last stable end product.
- Submit the form to view the result summary, table, and chart.
- Use the CSV or PDF buttons to export the calculated results.
FAQs
1) What does this calculator estimate?
It estimates how a parent nuclide decays into successive daughters over a chosen time. You get remaining amount, daughter buildup, activity, mass, and percentage share for each stage.
2) Can I enter grams instead of atoms?
Yes. Choose grams as the input unit and provide the parent molar mass. The calculator converts mass to atoms internally, then computes amounts for every stage.
3) What does branch fraction mean?
Branch fraction is the percentage of decays that feed the next listed nuclide. A value below 100% means some decays leave the modeled chain and are not tracked further here.
4) Can the final stage be stable?
Yes. Set the final half-life to zero. The calculator then treats that stage as stable accumulation, so it receives inflow from the previous stage without further decay.
5) Why do daughter amounts first rise and then fall?
A daughter nuclide increases while it is produced faster than it decays. Later, its own decay rate can overtake inflow, causing the amount to peak and then decline.
6) What is activity in this result table?
Activity is the decay rate in becquerels. One becquerel equals one disintegration per second. Higher activity means more nuclear transformations are happening each second.
7) Is this suitable for teaching and lab planning?
Yes. It is useful for demonstrations, quick scenario checks, and preparation work. For regulated applications, always confirm assumptions, isotopic data, and units before relying on final values.
8) Why might my totals not match perfectly?
Small differences can appear because branch losses remove material from the modeled chain and numerical integration uses finite time steps. Increasing stage accuracy usually improves agreement.