Calculate radioactive decay: find remaining quantity, time elapsed, or half-life using the formula N(t) = N₀ × (½)^(t/t½).
Given N₀, half-life t½, and time t → find remaining N(t).
| Property | Value |
|---|---|
| Remaining N(t) | 250 |
| Decayed | 750 |
| % Remaining | 25% |
| Half-lives elapsed | 2 |
| Decay constant λ | 0.69314718 |
| Mean lifetime τ | 1.442695 |
| Property | Formula |
|---|---|
| Remaining quantity | N(t) = N₀ × (½)^(t/t½) |
| Exponential form | N(t) = N₀ × e^(−λt) |
| Decay constant | λ = ln(2) / t½ |
| Half-life | t½ = ln(2) / λ |
| Mean lifetime | τ = 1/λ = t½ / ln(2) |
| Time elapsed | t = t½ × log₂(N₀/N(t)) |
| Isotope | Half-Life | Application |
|---|---|---|
| ¹⁴C | 5,730 years | Radiocarbon dating |
| ²³⁵U | 703.8 million yr | Nuclear fuel/dating |
| ²³⁸U | 4.47 billion yr | Rock age dating |
| ⁴⁰K | 1.25 billion yr | Geologic dating |
| ⁶⁰Co | 5.27 years | Medical/industrial |
| ¹³¹I | 8.02 days | Thyroid therapy |
| ¹³⁷Cs | 30.17 years | Industrial gauges |
| ²²²Rn | 3.82 days | Indoor air quality |
| ³H | 12.32 years | Self-lit devices |
| ⁹⁰Sr | 28.8 years | Beta source, RTGs |
Calculate half-life, remaining quantity, or elapsed time for any exponential decay process with our free calculator, commonly used in chemistry, physics, and nuclear science.
N(t) = N₀ × (1/2)^(t/T), where N₀ is the initial quantity, t is elapsed time, and T is the half-life. This calculator can solve for any of these variables given the other three.
Half-life is the time required for a quantity (commonly a radioactive substance) to reduce to half its initial value, a constant specific to each substance.
Yes, the same exponential decay math applies to drug elimination in pharmacology, capacitor discharge in electronics, and various other decay processes.
Because the decay rate is proportional to the remaining quantity, as less material remains, less decays in absolute terms per unit time, even though the percentage decay rate stays constant.
No, average lifetime (mean lifetime) is a related but distinct concept, typically about 1.44 times the half-life for exponential decay processes.