How old is a specimen with 30% Potassium-40 (⁴⁰K) remaining?
⚡ Instant Calculated Answer
A specimen containing 30% remaining Potassium-40 (⁴⁰K) has an age of exactly 2.168 Ga (representing 1.74 half-lives elapsed since closure).
2.168 Ga
Primary Metric
1.74 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 = 30% = 0.3.
- Take natural logarithm of fraction: ln(0.3) = -1.20397.
- Apply decay constant lambda = ln(2) / T_1/2 = 5.554e-10 yr⁻¹.
- Compute age: t = --1.20397 / (5.554e-10) = 2.168 Ga.
📊 Nearby Parameter Reference Table
| Isotope Remaining | Half-Lives Elapsed | Calculated Age |
|---|---|---|
| 36.0% | 1.47 | 1.839 Ga |
| 33.0% | 1.6 | 1.996 Ga |
| 30.0% | 1.74 | 2.168 Ga |
| 27.0% | 1.89 | 2.357 Ga |
| 24.0% | 2.06 | 2.569 Ga |
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