Half-Life Calculator
Calculate radioactive decay using exponential decay formulas and half-life principles
Calculate Radioactive Decay
Custom Half-Life
Amount of substance at time t = 0
Time period for decay calculation
Decay Calculation Results
Formula Used: N(t) = N₀ × 0.5^(t/t₁/₂)
Half-Life: Not set
Stability: Highly unstable
Common Radioactive Isotopes
Carbon-14 (C-14)
Half-life: 5,730 years
Beta decay • Radiocarbon dating, Archaeological studies, Geology
Uranium-238 (U-238)
Half-life: 4.468 billion years
Alpha decay • Nuclear fuel, Dating rocks, Nuclear weapons
Uranium-235 (U-235)
Half-life: 704 million years
Alpha decay • Nuclear reactors, Nuclear weapons, Fission fuel
Plutonium-239 (Pu-239)
Half-life: 24,110 years
Alpha decay • Nuclear weapons, Nuclear reactors, Space missions
Radium-226 (Ra-226)
Half-life: 1,600 years
Alpha decay • Medical treatments, Luminous paints, Research
Half-Life Scale
< 1 second
Very Short
Extremely unstable
1 sec - 1 hour
Short
Unstable
1 hour - 1 year
Medium
Moderately stable
1 - 1000 years
Long
Stable
> 1000 years
Very Long
Very stable
Decay Types
Applications
Understanding Half-Life and Radioactive Decay
What is Half-Life?
Half-life is the time required for half of the radioactive nuclei in a sample to decay. It's a fundamental property of each radioactive isotope and remains constant regardless of the initial amount of material or environmental conditions.
Key Concepts
- •Exponential Decay: Radioactive decay follows first-order kinetics
- •Probabilistic: Individual nuclei decay randomly, but large samples are predictable
- •Constant Rate: Half-life is independent of initial quantity
Decay Equations
Exponential Decay
N(t) = N₀ × 0.5^(t/t₁/₂)
N(t) = Remaining quantity at time t
N₀ = Initial quantity
t₁/₂ = Half-life
t = Elapsed time
Using Decay Constant
N(t) = N₀ × e^(-λt)
λ = Decay constant = ln(2)/t₁/₂
τ = Mean lifetime = 1/λ
Half-Life Formula
t₁/₂ = ln(2)/λ = τ × ln(2)
Relationship between half-life, decay constant, and mean lifetime
Applications and Examples
Carbon Dating
Uses C-14 half-life (5,730 years) to determine the age of organic materials up to 50,000 years old.
Nuclear Medicine
Tc-99m (6 hour half-life) used for medical imaging because it decays quickly after the procedure.
Nuclear Waste
Understanding half-lives helps manage radioactive waste and plan storage for thousands of years.
Practical Example: Carbon-14 Dating
Problem Setup
Initial C-14: 100% (living organism)
Current C-14: 25% (archaeological sample)
Half-life: 5,730 years
Calculation
25% = 100% × 0.5^(t/5730)
0.25 = 0.5^(t/5730)
t = 11,460 years (2 half-lives)