Activity ↔ mass
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Choose a nuclide and enter the mass or activity.
The specific activity of a nuclide links its mass to its activity: a = (ln2 / T½) · N_A / M, where T½ is the half-life, N_A the Avogadro number and M the molar mass. The sample activity is A = m · a, and the required mass is m = A / a. The calculator works for any of the 3561 nuclides in the database: pick a nuclide, enter the mass to get activity, or vice versa. It generalises the uranium and plutonium calculators to an arbitrary radionuclide.
The half-life is taken from the active nuclear database (ENDF/B-VIII.0, NNDC). The molar mass is taken as the mass number A of the nuclide — the systematic error from the mass defect is under 0.1%, less than the typical half-life uncertainty. Specific activity is given in Bq/g; the shorter the half-life and the lighter the atom, the higher it is (Tc-99m is around 10¹⁷ Bq/g, long-lived U-238 about 10⁴ Bq/g).
Converting mass to activity and back is needed when ordering and accounting for sources, estimating the mass of a radioactive substance for a target activity, in incoming inspection and work planning. For a producer and supplier of isotope products it is a basic calculation: how much substance matches the required source activity and what the specific activity of a batch is.
The calculation is for the bare nuclide without daughter ingrowth — for nuclides with short-lived daughters (Cs-137/Ba-137m, Sr-90/Y-90) the actual source emission is higher. Stable nuclides and nuclides without half-life data have no activity. For regulatory accounting and radiation-safety decisions, use the source certificate and accredited procedures.
About 0.88 mg: the specific activity of Co-60 is ≈ 4.19·10¹³ Bq/g (1131 Ci/g). For Cs-137 1 Ci is 11.5 mg, for Am-241 291 mg and for Ra-226 roughly 1 g.
m = A·M/(λ·N_A), where λ = ln2/T½, M is the molar mass (≈ mass number) and N_A is the Avogadro constant. Specific activity is a = λ·N_A/M and the mass is m = A/a.
The mass-defect error stays below 0.5 % even for H-3 and below 0.1 % for heavy nuclides — far smaller than the uncertainty of half-lives and certificate activities.