Atomic structure

Radioactivity is over a century old, yet it still treats cancer, powers grids and demands strict safety rules. This reference covers AQA GCSE Physics 8463, topic 4.4 Atomic structure.

How the exam treats this topic:

• Paper 1 (4.1–4.4) carries this topic. No equation sheet entries beyond energy; the work is notation, balancing and reasoning.
• Background radiation, half-life hazards, uses and fission/fusion are physics only.
• Net-decline ratios after several half-lives are Higher Tier.
• You must write balanced nuclear equations for single alpha and beta decay (balance atomic numbers and mass numbers; daughter naming not required).

An atom is very small: radius about $1\times10^{-10}$ m. Its structure:

• a positively charged nucleus containing protons and neutrons, surrounded by negatively charged electrons;
• the nucleus's radius is less than 1/10 000 of the atom's radius, yet it holds most of the mass;
• electrons sit at different distances (energy levels); absorbing electromagnetic radiation moves an electron further from the nucleus (higher level), emitting radiation moves it closer.

Notation: $\ ^{A}_{Z}X$ where $Z$ = atomic number (protons) and $A$ = mass number (protons + neutrons). In a neutral atom, electrons = protons; atoms have no overall charge.

• Isotopes 同位素: atoms of the same element (same $Z$) with different numbers of neutrons (different $A$).
• Neutrons in the nucleus = $A - Z$.
• Atoms that lose one or more outer electrons become positive ions.

Worked example. Carbon-14: $\ ^{14}_{6}\text{C}$.

• Protons = 6; electrons = 6 (neutral); neutrons = $14 - 6 = 8$.
• Carbon-12 has 6 neutrons — same element, different neutrons: isotopes.

New experimental evidence can change or replace a scientific model:

1. Before the electron's discovery: atoms were tiny spheres that could not be divided.
2. Electron discovered → the plum pudding model: a ball of positive charge with negative electrons embedded in it.
3. Alpha scattering (Rutherford): most alpha particles passed straight through, a few bounced back → the mass and positive charge must be concentrated in a tiny centre → the nuclear model replaced the plum pudding model.
4. Bohr adapted it: electrons orbit at specific distances; his calculations agreed with observations.
5. Further work showed the positive charge comes in whole-number units — the proton; Chadwick's experiments (about 20 years later) proved the neutron.

Why the scattering changed the model (each clause a mark): if the pudding were right, alpha particles should all pass through with small deflections (B1); some bounced almost straight back (B1), which is only possible if the mass and positive charge sit in a tiny, dense, positive nucleus (B1).

Some nuclei are unstable. They give out radiation as they change to become more stable — a random process called radioactive decay 放射性衰变.

• Activity 放射性活度: the rate at which a source decays; unit becquerel 贝克勒尔 (Bq).
• Count-rate 计数率: decays per second recorded by a detector (e.g. a Geiger–Muller tube).

Choose a source for a use by matching these properties: alpha for smoke alarms (stopped by smoke, safe when sealed); beta for thickness control of thin sheets (passes through and is partially absorbed); gamma for tracing and sterilising (penetrates the body).

Balance mass numbers (top) and atomic numbers (bottom) on both sides:

• Alpha decay: the nucleus loses 4 from the top and 2 from the bottom.
  $$^{238}_{\ 92}\text{U} \rightarrow\ ^{234}_{\ 90}\text{Th} +\ ^{4}_{2}\text{He}$$
• Beta decay: a neutron turns into a proton; mass number unchanged, atomic number +1; the beta particle is $\ ^{0}_{-1}\text{e}$.
  $$^{14}_{\ 6}\text{C} \rightarrow\ ^{14}_{\ 7}\text{N} +\ ^{0}_{-1}\text{e}$$
• Gamma emission: changes neither number.

Worked example. Polonium-210 decays by alpha emission. Write the equation.

• Alpha removes 4 and 2: $A: 210 - 4 = 206$; $Z: 84 - 2 = 82$.
  $$^{210}_{\ 84}\text{Po} \rightarrow\ ^{206}_{\ 82}\text{X} +\ ^{4}_{2}\text{He}$$
• Check both rows balance ✓ (the daughter's name is not required).

Decay is random: it cannot be predicted for any one nucleus; only the average behaviour of many is predictable.

Half-life 半衰期: the time for (a) the number of nuclei of the isotope in a sample to halve, or (b) the count rate / activity to fall to half its initial level.

• From a graph: read the time for the count rate to halve — repeat over several halvings and average.
• After $n$ half-lives, the fraction remaining is $1/2^n$ (HT: express as a ratio).

Worked example. A sample's count rate falls from 800 Bq to 200 Bq in 12 years.

• Halvings: $800 \to 400 \to 200$ is two halvings.
  $$t_{1/2} = \frac{12\ \text{years}}{2} = 6\ \text{years}$$

• Contamination 污染: unwanted radioactive atoms on an object. The hazard lasts as long as the atoms are there, decaying on or in the body.
• Irradiation 辐照: exposing an object to radiation. The irradiated object does not become radioactive.

Comparing the hazards (a credited pair): contamination gives a longer-lasting dose because the atoms stay and decay inside or on you, so the type of radiation matters (alpha is most dangerous inside the body); irradiation stops the moment the source is removed or shielded.

Precautions: hold sources with tongs, keep them at a distance, limit time near them, point them away from people, store in lead-lined boxes. Findings on radiation effects are published and peer-reviewed so they can be checked.

Background radiation 本底辐射 is around us all the time:

• natural: rocks (radon gas), cosmic rays from space, food, medical (natural body potassium);
• man-made: fallout from weapons testing, nuclear accidents, medical uses.

Dose depends on occupation and location (high altitude, certain industries). Dose unit: sieverts (1000 mSv = 1 Sv; recall not required).

Measurements of a sample must subtract the background count-rate first.

Half-life and hazard: a very long half-life stays active for thousands of years (waste storage problem); a very short half-life is intensely active while it lasts. Choose sources to match: medical tracers need short half-lives (the dose ends quickly); smoke alarms use a long half-life source so the alarm works for years.

Medical uses (each = exploration or destruction):

• Exploration: a gamma-emitting tracer (e.g. technetium-99m) injected so organs show on a scan; gamma escapes the body; short half-life limits dose.
• Destruction: focused gamma beams or implanted sources kill cancer cells (radiotherapy); beta for skin conditions.

Evaluating risk: compare the dose and consequence of the procedure against the risk of the illness — with numbers from the question.

Fission 核裂变: the splitting of a large, unstable nucleus (uranium-235, plutonium-239).

• Spontaneous fission is rare: the nucleus usually absorbs a neutron first.
• It splits into two smaller nuclei of roughly equal size, releasing two or three neutrons and gamma rays; energy is released and all products carry kinetic energy.
• The released neutrons can cause further fissions — a chain reaction. A reactor controls it (control rods absorb neutrons); a weapon's explosion is an uncontrolled chain.
• You must draw or interpret the diagram: neutron in → two fragments + neutrons out → branching chain.

Fusion 核聚变: two light nuclei join to form a heavier nucleus; some mass converts into the energy of radiation. Fusion releases more energy per kilogram than fission with no long-lived waste, but needs extreme temperature and pressure — why reactors are hard to build.

• Compute protons, neutrons, electrons from $A$ and $Z$; identify isotopes.
• Tell the atomic-model story in order and say what evidence changed it.
• Match α/β/γ to penetration, range and ionising power; choose sources for uses.
• Balance nuclear equations for single alpha and beta decay.
• Find a half-life from a graph or from two count rates; (HT) compute net decline.
• Distinguish contamination from irradiation and compare their hazards.
• (physics only) Background sources; half-life choice for hazard and use; medical exploration/destruction; fission chain vs fusion.