Half-life and radioactive decay rates
Radioactive decay is random for any single unstable nucleus: there is no way to predict when a particular atom will decay. But in a large sample, a predictable fraction decays over any given time. The half-life is the time it takes for half of the radioactive nuclei in a sample to decay. After one half-life, 1/2 of the original nuclei remain; after two, 1/4; after three, 1/8; and so on. Each isotope has its own half-life, which ordinary changes in temperature, pressure, or chemical bonding leave essentially unchanged (only a few rare kinds of decay show tiny effects): about 8 days for iodine-131, about 5,730 years for carbon-14, and about 4.5 billion years for uranium-238. Knowing an isotope's half-life lets scientists date ancient materials, since measuring how much of the isotope remains, compared with how much was there at the start, tells how many half-lives have passed. Half-lives also guide medical and safety decisions: medical imaging uses isotopes with short half-lives so they decay soon after use, while spent nuclear fuel contains long-lived isotopes that must be stored safely for thousands of years.
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