How old is a specimen with 25% Rubidium-87 (⁸⁷Rb) remaining?
⚡ Instant Calculated Answer
A specimen containing 25% remaining Rubidium-87 (⁸⁷Rb) has an age of exactly 97.6 Ga (representing 2.0 half-lives elapsed since closure).
97.6 Ga
Primary Metric
2.0 Half-Lives
Secondary Metric
📐 Mathematical Formula & Step-by-Step Substitution
- Identify the isotope half-life: T_1/2 = 48,800,000,000 years (48.8 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 = 1.420e-11 yr⁻¹.
- Compute age: t = --1.38629 / (1.420e-11) = 97.6 Ga.
📊 Nearby Parameter Reference Table
| Isotope Remaining | Half-Lives Elapsed | Calculated Age |
|---|---|---|
| 30.0% | 1.74 | 84.764 Ga |
| 27.5% | 1.86 | 90.89 Ga |
| 25.0% | 2.0 | 97.6 Ga |
| 22.5% | 2.15 | 105.018 Ga |
| 20.0% | 2.32 | 113.31 Ga |
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