Radioactivity & Particles

The Nuclear Model of the Atom

Everything is built from atoms, and every atom has a tiny, dense nucleus at its centre surrounded by orbiting electrons. The nucleus contains two kinds of particle, together called nucleons: protons and neutrons. The atom is mostly empty space — if the nucleus were the size of a marble, the nearest electron would be hundreds of metres away.

The table below summarises the three sub-atomic particles. Charges are given relative to the proton, and masses relative to the proton.

A neutral atom has equal numbers of protons and electrons, so the charges cancel. Because electrons are about 1840 times lighter than nucleons, almost all the mass of an atom is concentrated in the nucleus.

Key terms Atomic (proton) number $Z$ — the number of protons in the nucleus. It defines which element the atom is.

Mass (nucleon) number $A$ — the total number of protons and neutrons in the nucleus.

Isotopes — atoms of the same element (same $Z$) with different numbers of neutrons (different $A$).

We write a nuclide as $^{A}_{Z}\text{X}$. For example, carbon-14 is $^{14}_{6}\text{C}$: 6 protons, and $14 - 6 = 8$ neutrons.

To find the number of neutrons, use:

$$\text{neutrons} = A - Z$$

Isotopes behave identically in chemical reactions because they have the same number of electrons, but some isotopes are unstable and decay — these are radioactive.

Exam tip The big number is always the mass number $A$ (top), the small number is the proton number $Z$ (bottom). Neutrons are the difference. A favourite question gives you two nuclides and asks "are these isotopes?" — check that $Z$ matches but $A$ differs.

Background Radiation

We are exposed to background radiation all the time — a low level of radiation present everywhere. When measuring a radioactive source you must subtract this background count to get a true reading.

The main sources are:

Radon gas from rocks and soil (the largest source in most homes)
Rocks and buildings containing uranium, thorium and potassium
Cosmic rays from the Sun and outer space
Food and drink (naturally contains radioactive isotopes)
Medical sources, e.g. X-rays and scans
Nuclear weapons fallout and industry (a very small contribution)

Most background radiation is natural; only a small fraction is man-made.

The Three Types of Nuclear Radiation

Unstable nuclei become more stable by emitting radiation. There are three types: alpha ($\alpha$), beta ($\beta$) and gamma ($\gamma$).

Notice the pattern: the most ionising radiation (alpha) is the least penetrating, because it gives up its energy quickly as it smashes into atoms. Gamma is the most penetrating but least ionising.

Deflection in fields. Because alpha and beta are charged, they are deflected by electric and magnetic fields, while gamma (uncharged) passes straight through.

Alpha is positive, so it deflects towards the negative plate — but only slightly, as it is heavy.
Beta is negative, so it deflects towards the positive plate — and far more, in the opposite direction, as it is light.
Gamma is undeflected.

Watch out In a magnetic field, alpha and beta curve in opposite directions (they have opposite charge), and beta curves much more sharply because it is far lighter. Gamma goes straight on. Examiners love a diagram where you must label which track is which.

Nuclear Equations

In any nuclear decay, the totals of mass number and proton number are conserved — they must balance on both sides.

Alpha decay removes 2 protons and 2 neutrons, so $A$ drops by 4 and $Z$ drops by 2:

$$^{A}_{Z}\text{X} \;\rightarrow\; ^{A-4}_{Z-2}\text{Y} \;+\; ^{4}_{2}\alpha$$

For example, uranium decaying to thorium:

$$^{238}_{\;92}\text{U} \;\rightarrow\; ^{234}_{\;90}\text{Th} \;+\; ^{4}_{2}\alpha$$

Beta decay happens when a neutron turns into a proton and emits an electron. The mass number is unchanged, but the proton number rises by 1:

$$^{A}_{Z}\text{X} \;\rightarrow\; ^{\;\;\;A}_{Z+1}\text{Y} \;+\; ^{\;\;0}_{-1}\beta$$

For example, carbon-14 decaying to nitrogen:

$$^{14}_{\;6}\text{C} \;\rightarrow\; ^{14}_{\;7}\text{N} \;+\; ^{\;\;0}_{-1}\beta$$

Gamma emission carries away energy only, so it changes neither $A$ nor $Z$ — it usually follows alpha or beta decay as the nucleus settles down.

Half-life

Radioactive decay is a random process: we cannot predict when any individual nucleus will decay, but with huge numbers of nuclei the average behaviour is very predictable.

Key terms Activity — the number of nuclear decays per second, measured in becquerel (Bq).

Half-life — the average time taken for half the unstable nuclei in a sample to decay (equivalently, the time for the activity to halve).

A decay curve plots count rate (or number of nuclei) against time. It falls steeply at first then flattens, always halving over each half-life. It never quite reaches zero.

Worked example A sample has an activity of $800\ \text{Bq}$. Its half-life is $5\ \text{years}$. What is its activity after $15\ \text{years}$?

Number of half-lives $= 15 \div 5 = 3$.

Halve the activity three times:

$800 \rightarrow 400 \rightarrow 200 \rightarrow 100$

Exam tip To read half-life off a graph: pick a starting count, halve it, read across to the curve and down to the time axis. Doing this from two different starting points should give the same half-life — a good way to check your answer. Always subtract background count first.

Detecting Radiation

A Geiger–Müller (GM) tube connected to a counter is the standard detector. Radiation entering the tube ionises the gas inside, producing a pulse of current that registers as a "count". The reading is given as a count rate (counts per second or per minute).

Photographic film also detects radiation — it darkens on exposure, which is why people working with radiation wear film badges to monitor their dose.

Dangers, Safety and Uses

Dangers. Radiation is ionising: it can knock electrons off atoms in living cells, damaging or killing them and altering DNA, which can lead to mutations and cancer.

Outside the body, gamma (and beta) are the bigger hazard because they penetrate the skin; alpha is stopped by the outer dead skin layer.
Inside the body (if swallowed or inhaled), alpha is the most dangerous because it is intensely ionising and deposits all its energy in nearby tissue.

Safe handling:

Keep sources in lead-lined boxes; store well away from people.
Handle with long tongs, never with bare hands, to increase distance.
Limit exposure time and wear protective clothing/film badges.
Point sources away from the body.

Uses of radioactivity:

Real world Carbon dating uses carbon-14, which living things absorb while alive. After death the C-14 slowly decays with a half-life of about 5730 years. Measuring how much is left tells archaeologists the age of bones, wood and cloth. For much older rocks, isotopes with far longer half-lives, such as uranium, are used.

Nuclear Fission and Fusion

These two processes both release large amounts of energy from the nucleus.

Fission is the splitting of a large, unstable nucleus (such as uranium-235) into two smaller nuclei, releasing energy and several neutrons. Those neutrons can split further nuclei, causing a chain reaction — this is how nuclear power stations and atomic bombs work. In a reactor the chain reaction is controlled.

Fusion is the joining of two small, light nuclei (such as hydrogen isotopes) to form a larger nucleus, releasing huge amounts of energy. Fusion powers the Sun and stars. It requires extremely high temperatures and pressures to force the positive nuclei close enough together, which is why building a fusion power station on Earth is so difficult.

Watch out Don't mix them up: fission = splitting a big nucleus; fusion = fusing small nuclei together. Both release energy, but only fission produces the chain reaction used in today's power stations.