Isotope Half Life Time
Computes remaining mass of a radioactive isotope after N half-lives using decay law.
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Isotope half-life: N(t) = N₀·(1/2)^(t/T)
How much of a radioactive isotope is left after a time t follows N(t) = N₀·(1/2)^(t/T), which is the same thing as N(t) = N₀·e^(−λt) once you set the decay constant λ = ln(2)/T. Take N₀ = 100 g and t = 2T, and you're down to 25 g. The reference half-lives cover an enormous spread, around 24 orders of magnitude: Carbon-14 T = 5,730 years (radiocarbon dating up to ~50,000 yr, Libby 1949), Uranium-238 T = 4.47 Ga (Earth-age geochronology), Potassium-40 T = 1.25 Ga (K-Ar dating), Technetium-99m T = 6 h (the nuclear-medicine workhorse), Iodine-131 T = 8.02 days (thyroid therapy), Caesium-137 T = 30.17 yr (Goiânia 1987, Chernobyl 1986), Plutonium-239 T = 24,110 yr (reactors and weapons). The mean lifetime works out to τ = T/ln(2) ≈ 1.443·T.
Applications
Radiocarbon dating in archaeology and paleoclimatology, U-Pb and K-Ar geochronology of rocks and meteorites, nuclear medicine (Tc-99m scintigraphy, I-131 therapy, F-18 in PET), radioactive waste classification (in Brazil under CNEN/Law 10.308/2001), industrial radiography, and even the smoke detector sitting on your ceiling (Am-241, T ≈ 432 yr).
FAQ
Can half-life be changed? Not really. Decay happens in the nucleus, and it doesn't care about temperature, pressure, or what chemistry surrounds the atom. The rare exceptions show up with electron-capture isotopes under extreme conditions.
How many half-lives until "safe"? A rule of thumb people use is 10 half-lives, which leaves roughly 0.1 % of the activity. With long-lived isotopes that rule loses meaning, since what counts as "safe" hangs on the absolute activity level rather than how much time has gone by.
Why use Tc-99m if it lasts only 6 hours? That short half-life is exactly the point: it gives high specific activity for imaging and then clears the body fast, which keeps the patient's dose low. Hospitals make it on-site from Mo-99 generators.
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The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.