How old is a specimen with 50% Rubidium-87 (⁸⁷Rb) remaining?
⚡ Instant Calculated Answer
A specimen containing 50% remaining Rubidium-87 (⁸⁷Rb) has an age of exactly 48.8 Ga (representing 1.0 half-lives elapsed since closure).
48.8 Ga
Primary Metric
1.0 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 = 50% = 0.5.
- Take natural logarithm of fraction: ln(0.5) = -0.69315.
- Apply decay constant lambda = ln(2) / T_1/2 = 1.420e-11 yr⁻¹.
- Compute age: t = --0.69315 / (1.420e-11) = 48.8 Ga.
📊 Nearby Parameter Reference Table
| Isotope Remaining | Half-Lives Elapsed | Calculated Age |
|---|---|---|
| 60.0% | 0.74 | 35.964 Ga |
| 55.0% | 0.86 | 42.09 Ga |
| 50.0% | 1.0 | 48.8 Ga |
| 45.0% | 1.15 | 56.218 Ga |
| 40.0% | 1.32 | 64.51 Ga |
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