Radioactive Decay
Amount remaining after a number of half-lives.
Formula
Variables
Example
After 2 half-lives, 25% remains
How it works
Radioactive decay follows a predictable pattern: every half-life, the remaining amount is cut in half, not by a fixed amount but by a fixed fraction. That repeated halving is why the formula uses an exponent, with the number of half-lives equal to time divided by the half-life. It is useful whenever a substance or material decays at a constant proportional rate over time.
When to use it
Use this formula when you need to find how much of a radioactive isotope remains after some time, or to estimate how long it takes for a sample to decay to a certain fraction of its original amount. It is common in nuclear chemistry, geology, medical tracers, and environmental studies of contamination.
Worked example, step by step
A sample starts with 80 g of a radioactive substance with a half-life of 6 hours. How much remains after 15 hours? N = N0(1/2)^(t/t1/2) N = 80(1/2)^(15/6) N = 80(1/2)^2.5 N = 80 × 0.1768 N ≈ 14.1 g Final answer: about 14.1 g remains.
Common mistakes to avoid
- Using the half-life as the exponent instead of dividing elapsed time by half-life
- Subtracting half-life values from the initial amount instead of halving repeatedly
- Forgetting that the formula gives the remaining amount, not the amount lost
Did You Know?
Carbon-14 dating relies on its 5730-year half-life.
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