Physics / Unit 10: Magnetism and Modern Physics
10.6 Radioactivity and Half-Life
Notes
Unstable nuclei decay, giving off radiation.
| Radiation | What it is | Charge | Stopped by |
|---|---|---|---|
| alpha ($\alpha$) | helium nucleus, 2 protons + 2 neutrons | $+2$ | paper or skin |
| beta ($\beta$) | fast electron | $-1$ | thin aluminum |
| gamma ($\gamma$) | high-energy EM wave | 0 | thick lead or concrete |
- Alpha decay lowers $Z$ by 2 and $A$ by 4. Beta decay raises $Z$ by 1 and leaves $A$ unchanged.
- Half-life: the time for half of a radioactive sample to decay. After $n$ half-lives, $\displaystyle \left(\frac{1}{2}\right)^n$ remains.
- Example: 80 g of a substance with a 5-day half-life: after 15 days (3 half-lives), $\displaystyle 80 \times \frac{1}{8} = 10 \text{ g}$ remains.
Practice
A sample has a half-life of 2 hours. What fraction remains after 6 hours?
6 hours is 3 half-lives: $\displaystyle \left(\frac{1}{2}\right)^3 = \frac{1}{8}$.
Which type of radiation can be stopped by a sheet of paper?
Alpha particles are large and highly charged, so they are stopped easily.
Uranium-238 ($Z = 92$) undergoes alpha decay. What are the mass number and atomic number of the new nucleus?
Alpha decay removes 4 from $A$ and 2 from $Z$, giving thorium-234.
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