How old is a specimen with 25% Potassium-40 (⁴⁰K) remaining?
⚡ Instant Calculated Answer
A specimen containing 25% remaining Potassium-40 (⁴⁰K) has an age of exactly 2.496 Ga (representing 2.0 half-lives elapsed since closure).
2.496 Ga
Primary Metric
2.0 Half-Lives
Secondary Metric
📐 Mathematical Formula & Step-by-Step Substitution
- Identify the isotope half-life: T_1/2 = 1,248,000,000 years (1.25 Ga).
- Calculate remaining fraction N(t)/N_0 = 25% = 0.25.
- Take natural logarithm of fraction: ln(0.25) = -1.38629.
- Apply decay constant lambda = ln(2) / T_1/2 = 5.554e-10 yr⁻¹.
- Compute age: t = --1.38629 / (5.554e-10) = 2.496 Ga.
📊 Nearby Parameter Reference Table
| Isotope Remaining | Half-Lives Elapsed | Calculated Age |
|---|---|---|
| 30.0% | 1.74 | 2.168 Ga |
| 27.5% | 1.86 | 2.324 Ga |
| 25.0% | 2.0 | 2.496 Ga |
| 22.5% | 2.15 | 2.686 Ga |
| 20.0% | 2.32 | 2.898 Ga |
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