🎓 Chemistry • Atomic Chemistry
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Radioactive Half-Life Calculator
Computes radioactive decay N(t) = N0 · (1/2)^(t / t1/2) with isotope presets for Carbon-14, Iodine-131, and Uranium-238.
Common Radioisotopes & Nucli Presets1-click populate
Solve For Target Unknown:
Exponential Radioactive Decay: N(t) = N₀ · (½)^(t / t½)
Exponential Radioactive Decay Curve
Remaining Quantity N(t)
25 amount / grams
Remaining Fraction: 25% of original activity
Cycles Elapsed
2 t½
Decay Constant (λ)
1.2097e-4 / years
Mean Lifetime (τ)
8266.64 years
First-Order Kinetics Derivation
$N(t) = N_0 \times (0.5)^{\frac{t}{t_{1/2}}} = 100 \times (0.5)^{\frac{11460}{5730}} = 25.0000$
What is Half-Life?
Half-life is the time required for half of the radioactive atomic nuclei in a sample to undergo spontaneous nuclear decay.
Formula & Step-by-Step Calculation
N(t) = N₀ × (½)^(t / t½), λ = ln(2) / t½
Exponential nuclear decay law with decay constant λ.
Worked Step-by-Step Examples
Example 1
100g sample of Carbon-14 (t1/2 = 5730 years) after 11,460 years
Solution: 25.00 grams remaining (25.00%)
• 11,460 / 5730 = 2 half-lives ⟹ 100 × (0.5)² = 25.00 g
Common Real-World & Academic Use Cases
- ✓ Radiocarbon dating of fossils and artifacts
- ✓ Nuclear medicine radiopharmaceutical dosage timing
- ✓ Nuclear waste containment storage duration
How to Use the Radioactive Half-Life Calculator
1
Input Initial Amount & Half-Life
Enter N₀ and t½ or select an isotope preset.
2
Enter Elapsed Time
Input duration t.
3
Review Remaining Sample
Inspect remaining quantity, percentage, and decay constant.
Frequently Asked Questions
Q: Does half-life depend on initial mass?
No, radioactive half-life is an intrinsic constant for a given isotope and does not depend on sample size or temperature.