Half-Life
t½ = ln2/λ for first-order kinetics. Time for half of reactant to decay. Constant for nuclear decay and drug metabolism; depends on [A]₀ for zero- and second-order.
Why This Chemistry Calculation Matters
Why: Half-life governs radioactive decay, drug elimination, and reaction kinetics. First-order t½ is concentration-independent.
How: First-order: t½ = 0.693/k. Zero-order: t½ = [A]₀/(2k). Second-order: t½ = 1/(k[A]₀). After n half-lives: [A] = [A]₀(½)^n.
- ●First-order: C-14, I-131, drug elimination.
- ●Zero-order: constant rate; t½ depends on [A]₀.
- ●Second-order: t½ depends on initial concentration.
- ●After 5 half-lives ~3% remains; 10 half-lives ~0.1%.
Sample Examples
Input Parameters
For educational and informational purposes only. Verify with a qualified professional.
🔬 Chemistry Facts
t½ = ln2/λ ≈ 0.693/k. First-order only.
— IUPAC
Zero-order: t½ = [A]₀/(2k). Second-order: t½ = 1/(k[A]₀).
— Kinetics
After n half-lives: [A] = [A]₀ × (½)^n.
— NIST
Drug half-life: penicillin ~1 h; ibuprofen ~2 h.
— Pharmacology
What is Half-Life?
Half-life (t½) is the time required for the concentration of a reactant to decrease to half of its initial value. It is a fundamental concept in chemical kinetics, nuclear physics, and pharmacokinetics. For first-order reactions, half-life is constant and independent of initial concentration.
How to Calculate Half-Life
Zero-Order (n = 0)
t½ = [A]₀ / (2k)
Rate constant k in M/s.
First-Order (n = 1)
t½ = ln(2) / k = 0.693 / k
Most common for radioactive decay and drug elimination.
Second-Order (n = 2)
t½ = 1 / (k[A]₀)
Half-life depends on initial concentration.
When to Use Half-Life
- Radioactive Decay: C-14 dating, isotope stability
- Pharmaceuticals: Drug elimination, dosing intervals
- Chemical Kinetics: Reaction rates and mechanisms
- Environmental Science: Pollutant degradation
Key Formulas
| Zero-Order | t½ = [A]₀ / (2k) |
| First-Order | t½ = 0.693 / k |
| Second-Order | t½ = 1 / (k[A]₀) |
| After n half-lives (1st order) | [A] = [A]₀ × (1/2)^n |
| First-Order Decay | [A] = [A]₀ × e^(-kt) |
Remaining After n Half-Lives
First-order: [A] = [A]₀ × (1/2)^n. After 5 half-lives ~3% remains. After 10 half-lives ~0.1% remains.
❓ Frequently Asked Questions
Is half-life constant for all reaction orders?
Only for first-order. Zero-order and second-order half-lives depend on initial concentration.
📚 Official Data Sources
Important Notes
Radioactive decay follows first-order kinetics. Verify half-life values with NNDC or NIST for nuclear applications.
⚠️ Disclaimer: This calculator provides estimates for educational purposes. For nuclear decay, verify with NNDC or NIST. For pharmaceuticals, consult clinical references.
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