Definition and Formula
Half-life is defined as the amount of time it takes a given quantity to decrease to half of its initial value. The term is most commonly used in relation to atoms undergoing radioactive decay, but can be used to describe other types of decay, whether exponential or not.
Real-World Application: Carbon-14 Dating
One of the most well-known applications of half-life is carbon-14 dating. The half-life of carbon-14 is approximately 5,730 years, and it can be reliably used to measure dates up to around 50,000 years ago. Carbon-14 undergoes radioactive decay once a plant or animal dies, and measuring the amount of carbon-14 remaining conveys information about when the plant or animal died.
Key Variables
- N₀Initial quantity
- NₜRemaining quantity after time t
- t₁/₂Half-life
- τMean lifetime
- λDecay constant
Exponential Decay Formulas
The core relationship for exponential decay based on half-life is given by:
Other equivalent ways to express exponential decay involve the decay constant (λ) and the mean lifetime (τ):
Relationship Between Half-Life Constants
Using the equivalent formulas for exponential decay, we can derive a direct relationship between the Half-Life (t₁/₂), the Mean Lifetime (τ), and the Decay Constant (λ). If you know just one of these values, you can find the other two: