How old is a specimen with 50% Potassium-40 (⁴⁰K) remaining?
⚡ Instant Calculated Answer
A specimen containing 50% remaining Potassium-40 (⁴⁰K) has an age of exactly 1.248 Ga (representing 1.0 half-lives elapsed since closure).
1.248 Ga
Primary Metric
1.0 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 = 50% = 0.5.
- Take natural logarithm of fraction: ln(0.5) = -0.69315.
- Apply decay constant lambda = ln(2) / T_1/2 = 5.554e-10 yr⁻¹.
- Compute age: t = --0.69315 / (5.554e-10) = 1.248 Ga.
📊 Nearby Parameter Reference Table
| Isotope Remaining | Half-Lives Elapsed | Calculated Age |
|---|---|---|
| 60.0% | 0.74 | 919.73 Ma |
| 55.0% | 0.86 | 1.076 Ga |
| 50.0% | 1.0 | 1.248 Ga |
| 45.0% | 1.15 | 1.438 Ga |
| 40.0% | 1.32 | 1.65 Ga |
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