Activity from Number of Atoms Calculator

Activity From Number of Atoms: Technical Notes

1) What “activity” means in practice

Radioactive activity is the decay rate of a sample. In SI units, 1 Bq = 1 decay/s. Activity depends on how many unstable atoms are present and how quickly each atom is likely to decay. That “likelihood per second” is captured by the decay constant λ.

2) Core relationship used by this calculator

The calculator starts from A = λN. If you enter half‑life, it converts using λ = ln(2)/T½. This is useful because half‑life values are commonly tabulated, while λ is the parameter needed for direct activity calculations.

3) Time dependence and remaining atoms

When elapsed time is included, the remaining atoms follow N(t)=N₀e^−λt. The activity then becomes A(t)=λN(t). For example, after one half‑life, N halves and activity also halves. After two half‑lives, both drop to one quarter.

4) Unit handling and conversions

Time can be entered in seconds, minutes, hours, or days and is converted internally to seconds. Activity can be displayed in Bq, kBq, MBq, GBq, or Ci. The conversion used is 1 Ci = 3.7×10¹⁰ Bq, which helps compare modern SI results with legacy specifications.

5) Typical magnitudes you may encounter

Educational samples might be a few kBq to MBq, while medical tracers can be hundreds of MBq. Industrial gauges and research sources may reach GBq or higher depending on isotope and shielding. Because A scales linearly with N, doubling the number of atoms doubles activity at the same λ.

6) From mass to atoms (optional workflow)

If you start from mass, convert to atoms using N = (m/M)N_A, where M is molar mass and N_A is Avogadro’s constant. Once you have N, this calculator gives activity immediately. This is a common lab workflow for estimating activity from prepared quantities.

7) Assumptions and limits

The model assumes a single decay constant and no production or branching corrections. If your nuclide has multiple decay modes, the effective activity for a specific radiation channel depends on branching ratios. For long measurements, also consider detector dead time, geometry, and self‑absorption.

8) Interpreting results with uncertainty

Small errors in half‑life or atom count can propagate directly into activity. A 2% uncertainty in N yields about 2% uncertainty in A, and a 2% uncertainty in T½ produces about 2% uncertainty in λ. For planning, report activity with an uncertainty band rather than a single value.

FAQs

1) Why does activity scale with the number of atoms?

Each unstable atom has the same decay probability per second for a given isotope. With more atoms present, more decays occur per second. That is why A = λN is linear in N.

2) Should I enter half-life or decay constant?

Use whichever value you trust most. Many references list half-life, so it is convenient. If you already have λ from a model or dataset, entering it avoids an extra conversion step.

3) What does Bq represent compared to Ci?

Bq is decays per second and is the SI unit. Ci is an older unit tied historically to radium and equals 3.7×10¹⁰ Bq. The calculator shows both for easy comparison.

4) If time is zero, what is the activity reported?

At t=0, the calculator reports the initial activity A₀ = λN₀. If you provide elapsed time, it also reports the decayed activity A(t) after that duration.

5) Why do my measured counts not match the activity?

Detectors measure counts, not activity directly. Efficiency, geometry, shielding, dead time, and background reduce observed counts. Convert activity to expected count rate using detector efficiency and measurement setup factors.

6) Can I use this for isotopes with branching decay?

Yes for total activity, if λ describes overall decay. For activity of a specific emitted radiation, multiply the total activity by the relevant branching ratio (or emission probability).

7) What input format is best for large numbers of atoms?

Scientific notation is recommended, such as 3.2e18. It reduces typing errors and keeps large values readable. The calculator accepts both standard decimals and scientific notation.