Radioactive Decay & Half-Life
Unstable atomic nuclei break apart at random, one by one, and there is no way to predict exactly when any single nucleus will decay. But across a large sample, the pattern is completely predictable: after one half-life, exactly half the original nuclei remain, and after each further half-life, half of what is left decays away.
N = N₀ · (½)^(t/t½)
- N — remaining amount (g): the amount of the substance still remaining at time t
- N₀ — initial amount (g): the amount present at the very start, when t equals zero
- t — elapsed time (s): how much time has passed since the start
- t½ — half-life (s): the time it takes for half of the sample to decay
An 80 gram sample of a radioactive isotope has a half-life of 5 days. How much is left after 10 days?
- N₀ = 80 g
- t½ = 5 days
- N = N₀ · (½)^(t/t½)
- N = 80 g · (½)^(10/5) = 80 g · (½)²
N = 20 g
The same 80 gram sample keeps decaying. How much is left after 15 days?
- 40 g
- 10 g
- 26.7 g
After 3 half-lives have passed, what fraction of the original sample is still left?
- 1/8
- 1/3
- 1/6