How old is a specimen with 20% Potassium-40 (⁴⁰K) remaining?
⚡ Instant Calculated Answer
A specimen containing 20% remaining Potassium-40 (⁴⁰K) has an age of exactly 2.898 Ga (representing 2.32 half-lives elapsed since closure).
2.898 Ga
Primary Metric
2.32 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 = 20% = 0.2.
- Take natural logarithm of fraction: ln(0.2) = -1.60944.
- Apply decay constant lambda = ln(2) / T_1/2 = 5.554e-10 yr⁻¹.
- Compute age: t = --1.60944 / (5.554e-10) = 2.898 Ga.
📊 Nearby Parameter Reference Table
| Isotope Remaining | Half-Lives Elapsed | Calculated Age |
|---|---|---|
| 24.0% | 2.06 | 2.569 Ga |
| 22.0% | 2.18 | 2.726 Ga |
| 20.0% | 2.32 | 2.898 Ga |
| 18.0% | 2.47 | 3.087 Ga |
| 16.0% | 2.64 | 3.3 Ga |
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