Chemistry / Unit 2: Atomic Structure
2.6 Half-Life, Fission and Fusion
Notes
The half-life is the time for half of a radioactive sample to decay.
- After $n$ half-lives, the amount left is $\displaystyle \text{start} \times \left(\frac{1}{2}\right)^n$.
- Example: 80 g with a half-life of 5 days. After 15 days (3 half-lives): $80 \rightarrow 40 \rightarrow 20 \rightarrow 10$ g.
- Carbon-14 (half-life 5730 years) is used to date once-living things.
- Fission splits a heavy nucleus (like U-235) into smaller ones; used in nuclear power plants.
- Fusion joins light nuclei (like hydrogen into helium); powers the Sun. Both release huge energy because a little mass becomes energy ($E = mc^2$).
Practice
A 64.0 g sample has a half-life of 8 hours. How much remains after 24 hours?
24 hours is 3 half-lives: $64.0 \rightarrow 32.0 \rightarrow 16.0 \rightarrow 8.0$ g.
A bone has $\displaystyle \frac{1}{4}$ of the carbon-14 it had when alive. The half-life of C-14 is 5730 years. How old is it?
$\displaystyle \frac{1}{4}$ remaining means 2 half-lives: $2 \times 5730 = 11{,}460$ years.
Which process powers the Sun?
In the Sun's core, hydrogen nuclei fuse into helium and release energy.
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