☢️ Nuclear Physics & Radiometric Dating
Radioactive Half-Life & Decay Calculator
Calculate remaining substance $N(t)$, elapsed time, radiometric age, and decay constant ($\lambda$) with built-in radioactive isotope presets.
🦴 Carbon-14 (5,730 yrs)
🌍 Uranium-238 (4.47B yrs)
🏥 Iodine-131 (8.02 days)
☢️ Cesium-137 (30.17 yrs)
🏠 Radon-222 (3.82 days)
🔬 Cobalt-60 (5.27 yrs)
Decay Parameters
grams / Bq / %
Remaining Quantity N(t)
25.000 (25.0%)
Decay Constant ($\lambda$)
1.21 × 10⁻⁴
Mean Lifetime ($\tau$)
8,266.6 yrs
Quantity Decayed
75.0% Decayed
💡 Radiometric Decay Equation:
$$N(t) = 100 \times (0.5)^{(11460 / 5730)} = 100 \times (0.5)^2 = 25.0$$
The Law of Radioactive Decay
Radioactive disintegration is a first-order stochastic process governed by:
$$N(t) = N_0 e^{-\lambda t} = N_0 \left(\frac{1}{2}\right)^{t / t_{1/2}}$$
- Decay Constant ($\lambda$): $$\lambda = \frac{\ln(2)}{t_{1/2}} \approx \frac{0.693147}{t_{1/2}}$$
- Mean Lifetime ($\tau$): $$\tau = \frac{1}{\lambda} = \frac{t_{1/2}}{\ln(2)}$$
- Radiometric Age Solver: $$t = -\frac{\ln(N(t) / N_0)}{\lambda}$$