Radioactive Decay Calculator

Because elapsed time appears inside the exponent of the decay equation (A = A₀e^(−λt)), so a given percentage change in elapsed time compounds multiplicatively on the remaining fraction, while the same percentage change to the initial activity only rescales the answer by that same percentage. Waiting twice as long does not remove twice as much activity -- it removes a much larger share, following the exponential curve rather than a straight line.

No. The Time Unit field only tells the calculator whether your Half-Life and Elapsed Time numbers are in seconds, minutes, hours, days, or years -- it is a unit label, not an independent physical quantity. Switching units without also rescaling the numbers you entered would describe a completely different physical scenario, so always keep Half-Life and Elapsed Time in the unit you selected.

Half-Lives Elapsed is simply elapsed time divided by the half-life, a dimensionless count of decay periods that have passed -- 1.0 means exactly one half-life, 3.32 means a bit over three. It is a convenient way to sanity-check results, since after exactly 1, 2, or 3 half-lives the remaining fraction should land at almost exactly 50%, 25%, or 12.5% regardless of the isotope.

The mean lifetime (τ = 1/λ) is the average time a single atom in the sample survives before decaying, and it is always about 44% longer than the half-life (τ = t½ / ln 2). Half-life describes when half the population is gone; mean lifetime describes the average individual atom's survival time, which statisticians and nuclear engineers use for different calculations, such as total dose integrals.

No -- it models a single radioactive species decaying at one constant rate. Many real-world isotopes decay into other radioactive isotopes that then decay again on their own schedule (a decay chain), and the activity of any one nuclide in that chain over time follows a more complex set of coupled equations than the simple exponential this calculator solves.