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Radioactive decay and half-life: activity, becquerels and curies

Radioactive decay is random for any single atom but perfectly predictable for large numbers of them. That predictability is what the half-life captures.

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Study text drafted from public-domain US government sources. Practice questions are reviewed before publication.

Half-life and activity

The half-life is the time for half of the radioactive atoms in a sample to decay. After one half-life 50 percent remains, after three 12.5 percent, after ten about 0.1 percent. The decay constant λ = ln 2 / T½ is the probability per unit time that an atom decays, and activity — decays per second — equals λ times the number of atoms. For the same number of atoms, a shorter half-life means higher activity.

Activity is measured in becquerels (one decay per second) or curies (3.7 × 10¹⁰ Bq, as defined in 10 CFR 20.1005). Common examples: cesium-137 has a half-life of about 30 years, cobalt-60 about 5.3 years and iodine-131 about 8 days. Half-lives are fixed nuclear properties and do not change with temperature, pressure or chemistry in any practical way.

What changes in decay

In alpha decay the nucleus loses two protons and two neutrons, so the atomic number drops by 2 and the mass number by 4 (radium-226 becomes radon-222). In beta-minus decay a neutron becomes a proton, so the atomic number rises by 1 while the mass number stays the same (Cs-137 becomes Ba-137). Gamma emission usually follows as the daughter nucleus sheds excess energy.

Daughters can themselves be radioactive, forming decay chains such as the uranium-238 series that produces radium and radon. When a long-lived parent feeds a short-lived daughter, the two reach secular equilibrium and have equal activities, as with Cs-137 and Ba-137m.

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Frequently asked questions

How long until a source is "gone"?
Decay is exponential, so it never reaches exactly zero. Ten half-lives reduce activity to about one-thousandth; whether that is negligible depends on the starting activity.
How many becquerels are in a curie?
3.7 × 10¹⁰ Bq, which is 37 GBq. So 1 mCi = 37 MBq and 1 µCi = 37 kBq.
Does heating a source change its half-life?
No. Half-life is a nuclear property and is not changed in any practical way by temperature, pressure or chemical form.
What is a decay chain?
A series of radioactive parents and daughters that continues until a stable nuclide is reached, for example the uranium-238 series ending at lead-206.

Sources

  1. 10 CFR Part 20, Standards for Protection Against Radiation (U.S. NRC) www.ecfr.gov
  2. DOE Fundamentals Handbook: Nuclear Physics and Reactor Theory, DOE-HDBK-1019/1-93 and DOE-HDBK-1019/2-93
  3. U.S. NRC Glossary (NRC Basic References) www.nrc.gov
  4. U.S. EPA, Radiation Basics www.epa.gov

Explanations on this page are original. Cited US government works are in the public domain; they do not endorse this site.