Chapter 17 · Radioactivity and Nuclear Chemistry
17.5Natural Radioactivity and Half-Life
12 min · two checks
Predict
If a sample’s half-life is 10 years, how much of the original isotope remains after 30 years?
The idea
- Use half-life to find what fraction remains.
- Explain why a shorter half-life means a higher decay rate.
Half-life, t½, is the time in which half of the radioactive nuclei decay. It is a property of the isotope, not of the sample size or the chemistry. After n half-lives the fraction left is (1/2)ⁿ. The amount left is N = N₀ (1/2)^(t / t½). A short half-life means the nuclei are eager to decay, so a given number of atoms produces more emissions per second. A long half-life means a sample stays active for ages but ticks slowly.
Decay series chain one unstable nucleus into another until a stable isotope appears. Uranium-238 ends, after many alphas and betas, at lead-206. Radon-222, a noble-gas isotope in that series, can seep from rock into basements; because it is a gas, it is inhaled, and its short-lived alpha-emitting daughters do their damage in the lung. Ventilation is the practical response. You cannot scrub radon out by a chemical reaction with the air.
Keep these
- Fraction left = (1/2)^(t / t½).
- Half-life does not depend on the amount.
- Shorter half-life means faster decay of each nucleus.
Worked path
Iodine-131 has a half-life of about 8.0 days. What fraction of a dose remains after 24 days?
Observe
Number of half-lives = 24/8.0 = 3.