Radioactivity

An atom is a tiny nucleus of protons (charge $+ 1$ ) and neutrons (charge $0$ ), surrounded by electrons (charge $- 1$ ). Almost all the mass is in the nucleus. The atomic number $Z$ is the number of protons; the mass number $A$ is protons + neutrons.

Isotopes have the same $Z$ but different $A$ . Nuclide notation writes both, e.g. carbon-14 as $_{6}^{14} C$ . Ionisation is the gain or loss of electrons.

An unstable nucleus emits radiation at random. The three types:

Alpha ( $α$ ): a helium nucleus $_{2}^{4} He$ ; $A$ falls by 4, $Z$ by 2.
Beta ( $β$ ): a fast electron from a neutron turning into a proton; $A$ unchanged, $Z$ up by 1.
Gamma ( $γ$ ): high-energy EM radiation; no change to $A$ or $Z$ .

Worked example

Complete the alpha decay $_{88}^{226} Ra \to ? +_{2}^{4} He$ .

Mass: $226 - 4 = 222$ . Proton number: $88 - 2 = 86$ (radon): $_{86}^{222} Rn .$

A chart showing alpha radiation stopped by paper, beta radiation stopped by aluminium, and gamma radiation only reduced by lead. — Alpha is stopped by paper, beta by a few mm of aluminium, gamma only by thick lead; alpha is the most strongly ionising despite its low penetration.

Penetration increases $α < β < γ$ (alpha is stopped by paper, beta by aluminium, gamma needs lead), but ionising ability is the reverse; alpha ionises most. In a field, $α$ and $β$ deflect in opposite directions (opposite charges) and $γ$ not at all. Background radiation is always present.

A radioactive decay curve showing the amount remaining halving over each successive half-life. — Each half-life the amount remaining halves; after n half-lives, a fraction (½)ⁿ is left.

The half-life is the time for half the nuclei (or the activity) to decay. After $n$ half-lives, the fraction remaining is $(\frac{1}{2})^{n}$ .

Worked example

A sample's activity is $800 Bq$ ; its half-life is $3 days$ . Find the activity after $9 days$ .

$9 days = 3$ half-lives, so $800 \times (\frac{1}{2})^{3} = 800 \times \frac{1}{8} = 100 Bq .$

Exam tip

Turn the elapsed time into a *number of half-lives* first, then just halve repeatedly. This is far quicker than any formula on a non-calculator paper.

Mixing up penetration with ionising power (they run in opposite orders).
Beta decay: $Z$ goes up by 1, mass number is unchanged.
Forgetting to convert the elapsed time into whole half-lives.

Atomic structure

Radioactive decay

Ionising radiation

Half-life

Common mistakes