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How It Works
Radioactive decay follows an exponential law: N(t) = N₀e−λt. The decay constant λ determines how quickly a material decays. Related quantities include the half-life (t½ = ln2/λ), mean lifetime (τ = 1/λ), and activity (A = λN). Each isotope has a unique half-life, from microseconds to billions of years.
Example Problem
Carbon-14 has a half-life of 5,730 years. If a sample originally contained 1,000 atoms, how many remain after 11,460 years?
- Number of half-lives: 11,460 / 5,730 = 2
- Remaining: 1,000 × (½)² = 1,000 × 0.25 = 250 atoms
Frequently Asked Questions
What is a half-life?
A half-life is the time it takes for half the atoms in a radioactive sample to decay. After two half-lives, one-quarter of the original atoms remain; after three, one-eighth, and so on.
What is the difference between half-life and mean lifetime?
The mean lifetime τ is the average survival time of an atom. It is always longer than the half-life by a factor of 1/ln(2) ≈ 1.443. Both are determined by the decay constant λ.
How is radioactive decay used in dating?
By measuring the ratio of a radioactive isotope to its decay product, scientists can calculate how long ago the material formed. Carbon-14 dating works for organic materials up to ~50,000 years old; uranium-lead dating covers billions of years.
Related Calculators
- Einstein Equation Calculator — calculate the energy released from mass conversion.
- Kinetic Energy Calculator — find the energy of emitted particles.
- Wien's Law Calculator — relate radiation wavelength to temperature.
- Natural Log Calculator — solve the exponential decay equation for time or half-life.
- Density Calculator — find the density of radioactive materials and shielding.
- Time Converter — convert half-life between seconds, years, and other time units.
Reference: Lindeburg, Michael R. 1992. Engineer In Training Reference Manual. Professional Publication, Inc. 8th Edition.