How old is a specimen with 60% Rubidium-87 (⁸⁷Rb) remaining?
⚡ Instant Calculated Answer
A specimen containing 60% remaining Rubidium-87 (⁸⁷Rb) has an age of exactly 35.964 Ga (representing 0.74 half-lives elapsed since closure).
35.964 Ga
Primary Metric
0.74 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 = 60% = 0.6.
- Take natural logarithm of fraction: ln(0.6) = -0.51083.
- Apply decay constant lambda = ln(2) / T_1/2 = 1.420e-11 yr⁻¹.
- Compute age: t = --0.51083 / (1.420e-11) = 35.964 Ga.
📊 Nearby Parameter Reference Table
| Isotope Remaining | Half-Lives Elapsed | Calculated Age |
|---|---|---|
| 72.0% | 0.47 | 23.128 Ga |
| 66.0% | 0.6 | 29.254 Ga |
| 60.0% | 0.74 | 35.964 Ga |
| 54.0% | 0.89 | 43.382 Ga |
| 48.0% | 1.06 | 51.674 Ga |
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