Half-life Calculator
Relationship between half-life and decay constant.
Formula first
Overview
The half-life represents the time required for a radioactive substance to diminish to one-half of its original quantity. It is a fundamental property of unstable atomic nuclei, where the decay rate is proportional to the number of atoms present, governed by the decay constant.
Symbols
Variables
T_{1/2} = Half-life, \lambda = Decay Constant
Apply it well
When To Use
When to use: Use this formula when modeling first-order decay processes where the probability of decay is constant per unit time. It is applicable for calculating the longevity of radioactive isotopes or determining the decay constant from observed temporal data.
Why it matters: Understanding half-life is essential for carbon dating ancient artifacts, managing nuclear waste safety, and calculating medical tracer dosages. It allows scientists to predict how long hazardous materials will remain active in a given environment.
Avoid these traps
Common Mistakes
- Using log10 instead of ln.
- Mixing seconds and years.
One free problem
Practice Problem
A radioactive isotope of Cobalt-60 used in medical radiotherapy has a decay constant (L) of 0.131 per year. Calculate its half-life (T) in years.
Solve for:
Hint: Divide the natural log of 2 (approximately 0.693) by the given decay constant.
The full worked solution stays in the interactive walkthrough.
References
Sources
- Halliday, Resnick, Walker - Fundamentals of Physics
- Wikipedia: Half-life
- Atkins' Physical Chemistry
- Halliday, Resnick, and Walker, Fundamentals of Physics
- Wikipedia: Carbon-14
- IUPAC Gold Book: Half-life
- Halliday, Resnick, Walker Fundamentals of Physics
- Edexcel A-Level Physics — Nuclear and Particle Physics