Radioactive Decay
N(t) = N₀e^(-λt) describes exponential decay of unstable nuclei. Half-life t½ = ln2/λ is constant for each isotope. Essential for nuclear medicine, radiocarbon dating, and radiation safety.
Why This Chemistry Calculation Matters
Why: Radioactive decay governs nuclear medicine dosing, archaeological dating, and radiation safety. First-order kinetics; half-life is isotope-specific.
How: N = N₀e^(-λt). λ = ln2/t½. Activity A = λN. After n half-lives, N = N₀(½)^n.
- ●C-14 half-life 5730 yr; U-238 ~4.5 billion yr.
- ●Activity in Bq (1 decay/s) or Ci (3.7×10¹⁰ Bq).
- ●Tc-99m (6 h) and I-131 (8 d) common in nuclear medicine.
- ●After 5 half-lives ~97% decayed; 10 half-lives ~99.9%.
Sample Examples
Input Parameters
For educational and informational purposes only. Verify with a qualified professional.
🔬 Chemistry Facts
N(t) = N₀e^(-λt). Exponential decay law.
— IUPAC
t½ = ln2/λ ≈ 0.693/λ. Constant for first-order.
— Nuclear chem
A = λN. Activity in Bq or Ci.
— NIST
After n half-lives: N = N₀(½)^n.
— Kinetics
What is Radioactive Decay?
Radioactive decay is the spontaneous process by which an unstable atomic nucleus loses energy by emitting radiation, transforming into a different element or isotope. The decay follows exponential kinetics: N = N₀ × e^(-λt).
Key: N₀ = initial nuclei, λ = decay constant, t = time, e = Euler's number (≈2.718)
How to Calculate Radioactive Decay
Exponential Decay: N = N₀ × e^(-λt)
λ = ln(2)/t½ = 0.693/t½. Activity: A = λN. Time elapsed: t = (1/λ) × ln(N₀/N)
Activity Units
1 Bq = 1 decay/s. 1 Ci = 3.7 × 10¹⁰ Bq
When to Use Radioactive Decay Calculations
- Radiocarbon dating (C-14)
- Nuclear medicine (I-131, Tc-99m)
- Radiation safety and handling times
- Nuclear physics and isotope stability
- Environmental contamination tracking
- Geological dating (U-238)
Types of Radioactive Decay
Alpha (α)
Helium nucleus emission. U-238 → Th-234 + α
Beta (β)
Electron/positron emission. C-14 → N-14 + β⁻
Gamma (γ)
Photon emission. No mass/atomic number change
Key Formulas
| Exponential Decay | N = N₀ × e^(-λt) |
| Decay Constant | λ = ln(2)/t½ |
| Half-Life | t½ = ln(2)/λ |
| Activity | A = λN |
| Time Elapsed | t = (1/λ) × ln(N₀/N) |
| After n Half-Lives | N = N₀ × (1/2)^n |
Practical Examples
Important Considerations
- First-order kinetics; half-life constant for each isotope
- After 5 half-lives ~97% decayed; after 10 ~99.9%
- Activity decreases exponentially: A = A₀ × e^(-λt)
- Decay constant units: s⁻¹
📚 Official Data Sources
⚠️ Disclaimer: Uses IUPAC/NNDC/NIST conventions. For critical applications consult accredited sources.
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