Half-Life
The time for half of a radioactive sample to decay.
About this topic
The half-life is the time for half of the radioactive nuclei in a sample to decay, or for the activity to halve. After n half-lives, the fraction left is (½)ⁿ. Carbon-14 has a half-life of 5730 years, iodine-131 about 8 days.
Example: a sample of iodine-131 with 80 g has 40 g after 8 days, 20 g after 16 days and 10 g after 24 days. The decay is exponential: N = N₀e^(−λt), with λ = ln 2 / t½. A graph of activity against time gives a smooth falling curve that never quite reaches zero.
Half-life underlies radiocarbon dating, medical tracer selection, where short half-lives limit patient dose, and nuclear waste management, where some isotopes stay dangerous for millennia. Archaeologists compare the carbon-14 left in a bone to that in living tissue to estimate its age.
A big misconception is that two half-lives mean everything has gone. In fact one quarter remains. Half-life does not depend on how much material you start with, nor on temperature or chemistry.
Key ideas
- Exponential decay
- After n half-lives, 1/2ⁿ remains
- Used in carbon dating
Quick check
Use cases: where Half-Life helps
- Homework: review the key idea behind Half-Life before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Half-Life without notes.
- Visual learning: play with the interactive lab to see how Half-Life changes when you adjust its inputs.
- Teaching a friend: explain Half-Life in your own words, then compare your version with the key ideas.
The same laws describe car crashes, sports, satellites and everyday machines.
Frequently asked questions
What is Half-Life?
The time for half of a radioactive sample to decay.
What will I learn in Half-Life?
Exponential decay. After n half-lives, 1/2ⁿ remains. Used in carbon dating.
Is Half-Life part of Physics?
Yes. It is one of 150 Physics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Half-Life lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Half-Life?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.