How it’s calculated
In first-order (radioactive) decay a fixed fraction decays per unit time, so half of what remains is gone after every half-life, however much you start with.
Example: 100 g of carbon-14 (t½ = 5,730 years) after 11,460 years is two half-lives, so N = 100 × (½)² = 25 g remain.
Frequently asked questions
Does a substance ever fully decay?
Mathematically the amount only approaches zero. After 10 half-lives about 0.1% remains, which is often treated as negligible.
How is carbon dating done?
Living things keep a steady C-14 level. After death it decays with a 5,730-year half-life, so the remaining fraction gives the age: t = t½ × log₂(N₀/N).
Does this work for drugs in the body?
Many drugs are eliminated with first-order kinetics, so the same formula gives an approximation. Follow medical advice for actual dosing.
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Sources
- Chemistry 2e, §21.3 Radioactive Decay — OpenStax
- College Algebra 2e, §6.7 Exponential and Logarithmic Models — OpenStax
Formulas are taken from the free public references above. Results are provided “as is” for informational and educational purposes only. See our disclaimer.
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