Enter your Initial Quantity (N₀), Time Elapsed, and Half-Life — or any combination of known values — into this Half-Life Calculator to find the Remaining Quantity, Decay Constant (λ), Mean Lifetime, and exactly what percentage of your sample has decayed or survived.
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Percentage Remaining
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Percentage Decayed
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Mean Lifetime
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Radioactive decay is the process by which unstable atomic nuclei emit particles or electromagnetic radiation to become more stable. This process occurs randomly but at a predictable average rate for any given isotope.
Half-life is the time required for exactly half of a radioactive substance to decay. It's a constant characteristic of each radioactive isotope and is independent of the initial amount of material.
Half-life can be calculated using the formula t₁/₂ = ln(2)/λ, where λ is the decay constant. Alternatively, if you know the initial and remaining quantities and time elapsed, you can use t₁/₂ = t × ln(2)/ln(N₀/N(t)).
Carbon-14 has a half-life of approximately 5,730 years. This makes it useful for dating organic materials up to about 50,000 years old through radiocarbon dating.
Uranium-238 has a half-life of about 4.47 billion years, making it one of the longest-lived radioactive isotopes. This extremely long half-life is why uranium can still be found naturally on Earth.
Mean lifetime is the average time a radioactive nucleus exists before decaying, calculated as 1/λ (where λ is the decay constant). It's related to half-life by the formula: mean lifetime = half-life / ln(2) ≈ 1.44 × half-life.
No, half-life is an intrinsic property of each radioactive isotope and cannot be altered by external conditions like temperature, pressure, or chemical environment. It depends only on the nuclear structure of the atom.