The formula
N = N₀ · (½)^(t / t½)
| Symbol | Quantity | Unit |
|---|---|---|
| N | Amount remaining | |
| N₀ | Initial amount | |
| t | Time elapsed | |
| t½ | Half-life |
What it means
Radioactive decay is exponential: a fixed proportion decays in each equal interval, not a fixed amount. The half-life is the time for half of whatever is present to decay, and it does not change as the sample shrinks.
How to work it out by hand
- Divide the elapsed time by the half-life
- That gives the number of halvings
- Halve the starting amount that many times
What is worth knowing
The counter-intuitive part is that a half-life is constant regardless of how much is left: a sample down to a millionth still halves in the same period. That is what makes radiometric dating work, and why carbon-14 with its 5730-year half-life is useful up to about 50,000 years and useless beyond — too little remains to measure. Half-lives span an extraordinary range, from fractions of a second to billions of years, and uranium-238's 4.5 billion years is roughly the age of the Earth, which is why there is still any left.