By David Robinson • Updated March 24, 2022
Radioactive elements decay at rates that were traditionally measured in curies. The International Council of Scientific Unions defines one curie as the activity of a substance that undergoes 3.7 × 10¹⁰ disintegrations per second. Because decay rates vary between elements, converting a mass in grams to curies is only possible when the exact isotope is known.
Find the atomic weight of the isotope from the periodic table. For example, Cobalt‑60 has an atomic weight of 59.92, while Uranium‑238 is 238.
Convert the mass to moles: moles = mass / atomic mass. Then multiply by Avogadro's number (6.02 × 10²³) to obtain the number of atoms. For instance, 1 g of Cobalt‑60 yields (1 / 59.92) × 6.02 × 10²³ ≈ 1.01 × 10²² atoms.
Calculate the decay rate (r) using the isotope’s activity. For Cobalt‑60 with an activity of 1.10 × 10³ Ci, r = activity × (3.700 × 10¹⁰ atoms s⁻¹ Ci⁻¹) = 4.04 × 10¹³ atoms s⁻¹.
Determine the decay constant (k) from the first‑order rate equation r = k × [number of atoms]. Using r = 4.04 × 10¹³ and 1.01 × 10²² atoms gives k ≈ 4.1 × 10⁻⁹ s⁻¹.
Compute the activity of the sample: activity = k × [number of atoms]. For 1.01 × 10²² atoms, activity = 4.1 × 10⁻⁹ s⁻¹ × 1.01 × 10²² ≈ 4.141 × 10¹³ atoms s⁻¹.
Convert the decay rate to curies by dividing by 3.7 × 10¹⁰. Thus 1 g of Cobalt‑60 corresponds to 4.141 × 10¹³ / 3.7 × 10¹⁰ ≈ 1,119 Ci.
Use a scientific calculator and perform all calculations in scientific notation to avoid errors from handling large numbers.
Step 4 involves calculus and requires advanced mathematical knowledge.
