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 |