Half-Life

Iodine-131, a fission product from nuclear reactors, has a half-life of 8 days. After Fukushima, iodine contamination in nearby seawater dropped to safe levels within weeks. Cesium-137, another fission product, has a half-life of 30 years. Cesium contamination from Chernobyl (1986) still prevents farming in parts of Belarus. Same process, wildly different timescales.

Half-life is the time it takes for half of a radioactive sample to decay. After one half-life, 50% remains. After two, 25%. After three, 12.5%. After ten half-lives, less than 0.1% remains. The decay is exponential: rapid at first, then increasingly slow.

Half-life is an intrinsic property of each isotope and cannot be changed by temperature, pressure, or chemistry. U-238 has a half-life of 4.5 billion years (roughly Earth's age). C-14 has 5,730 years (used for carbon dating). Plutonium-239 has 24,100 years. These numbers determine how long nuclear waste remains hazardous, which is the central issue in nuclear waste policy.

Worked Example

A spent fuel rod contains 1,000 grams of Cesium-137 (half-life: 30 years). After how many years will less than 1 gram remain?

• Calculate number of half-lives to reach <1 g. 1,000 → 500 → 250 → 125 → 62.5 → 31.25 → 15.6 → 7.8 → 3.9 → 1.95 → 0.98 g. That is 10 half-lives.
• Calculate time. 10 x 30 = 300 years.

Why does nuclear waste policy focus on storage timescales of hundreds to thousands of years?

Because the most hazardous fission products (Cs-137, Sr-90) have half-lives of ~30 years, requiring about 300 years (10 half-lives) to decay to negligible levels. Some actinides (Pu-239) require hundreds of thousands of years. The timescale depends on which isotopes are present.

This is also why the isotope mix inside spent fuel, not just its total mass, decides what "permanent" storage has to mean: a repository built for cesium's 300-year problem looks nothing like one built for plutonium's 24,100-year half-life.

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