What you'll learn
Atomic and nuclear physics is the final topic of CXC CSEC Physics and the one that looks inside the atom at what happens when a nucleus is unstable. It covers the historical development of the atomic model, the structure of the nucleus, the three types of radiation and how they differ, radioactive decay and half-life, and the release of energy by fission and fusion. It is also the topic where the mathematics is least demanding but the precision of language matters most: contamination and irradiation are different things, and decay is a random process that nevertheless follows a reliable statistical law. By the end of this guide you should be able to describe the atom's structure, explain how alpha scattering established the nuclear model, compare the three radiations, complete nuclear equations, perform half-life calculations, distinguish fission from fusion, and describe the hazards, safety precautions and uses of radioactivity.
Key terms and definitions
Nucleon — a proton or a neutron, the particles making up the nucleus
Atomic number — the number of protons in a nucleus, which identifies the element
Mass number — the total number of protons and neutrons in a nucleus
Isotope — an atom of the same element with the same number of protons but a different number of neutrons
Radioactivity — the spontaneous and random emission of radiation from an unstable nucleus
Alpha particle — a helium nucleus, consisting of two protons and two neutrons
Beta particle — a high-speed electron emitted from the nucleus when a neutron changes into a proton
Gamma ray — high-frequency electromagnetic radiation emitted from the nucleus, with no mass and no charge
Half-life — the time for half the undecayed nuclei in a sample to decay, or for the count rate to halve
Background radiation — the low-level radiation always present in the environment from natural and artificial sources
Irradiation — exposing an object to radiation, which does not make the object radioactive
Contamination — the presence of radioactive material on or inside another object
Fission — the splitting of a large nucleus into two smaller ones with the release of energy
Fusion — the joining of two small nuclei to form a larger one with the release of energy
Core concepts
The structure of the atom
An atom consists of a very small, dense, positively charged nucleus containing protons and neutrons, surrounded by electrons in shells.
Protons carry a relative charge of plus 1 with a relative mass of 1. Neutrons are uncharged with a relative mass of 1. Electrons carry a charge of minus 1 with negligible mass.
The nucleus contains almost all the mass of the atom but occupies only a tiny fraction of its volume, with a radius roughly one ten-thousandth that of the atom. The rest is empty space.
The atomic number is the number of protons and identifies the element. The mass number is protons plus neutrons, so the number of neutrons equals the mass number minus the atomic number.
Isotopes are atoms of the same element with different neutron numbers. They have identical chemical properties because their electron arrangements are the same, but differ in mass and in nuclear stability. Some isotopes of an element are stable while others are radioactive.
The alpha scattering experiment
The nuclear model replaced the earlier plum pudding model as a direct result of experiment, and this reasoning is examined.
Alpha particles were directed at a very thin sheet of gold foil, and their paths were observed.
Most passed straight through with little or no deflection, showing that the atom is mostly empty space.
A small number were deflected through large angles, showing that they had encountered a concentrated positive charge which repelled them.
A very few rebounded almost straight back, showing that this positive charge is concentrated in a very small volume containing most of the mass.
The conclusion was the nuclear model: a tiny, dense, positively charged nucleus with electrons occupying the space around it. The general principle worth stating is that a scientific model is revised when new experimental evidence cannot be explained by the existing one.
Radioactive decay
Some nuclei are unstable and emit radiation spontaneously to become more stable. The process is spontaneous, meaning it is not affected by external conditions such as temperature or pressure, and random, meaning it is impossible to predict which nucleus will decay next or when.
Because it is random, half-life is a statistical property applying to large numbers of nuclei rather than a prediction about any individual nucleus.
Activity is the number of decays per second, measured in becquerels, and count rate is what a detector such as a Geiger-Müller tube actually records.
The three types of radiation
An alpha particle is a helium nucleus with two protons and two neutrons, carrying a charge of plus 2 and having a relative mass of 4. It is the most strongly ionising of the three, precisely because it is massive and doubly charged, but for the same reason it loses energy rapidly and is the least penetrating. It is stopped by a sheet of paper or a few centimetres of air, and it is deflected by electric and magnetic fields.
A beta particle is a high-speed electron emitted from the nucleus when a neutron changes into a proton. It carries a charge of minus 1 and has negligible mass. It is moderately ionising and moderately penetrating, stopped by a few millimetres of aluminium, with a range of about a metre in air. It is deflected by fields in the opposite direction to alpha, and more strongly because of its much smaller mass.
A gamma ray is high-frequency electromagnetic radiation with no mass and no charge. It is the least ionising and the most penetrating, requiring several centimetres of lead or metres of concrete to reduce it significantly, and it has effectively unlimited range in air. Being uncharged, it is not deflected by electric or magnetic fields.
The general pattern is that the more strongly ionising a radiation is, the less far it penetrates, because it gives up its energy to the material more rapidly.
Nuclear equations
In any nuclear equation, both the mass number and the atomic number must balance on each side.
Alpha decay reduces the mass number by 4 and the atomic number by 2, because two protons and two neutrons leave the nucleus. The element changes.
Beta decay leaves the mass number unchanged and increases the atomic number by 1, because a neutron has become a proton. The element changes.
Gamma emission changes neither the mass number nor the atomic number, because a gamma ray has no mass and no charge. Only the energy of the nucleus decreases, and gamma emission usually accompanies alpha or beta decay rather than occurring alone.
Half-life
The half-life of a radioactive isotope is the time taken for half the undecayed nuclei in a sample to decay, or equivalently for the count rate to fall to half its value.
Calculations follow a simple pattern of repeated halving. After one half-life, half the original nuclei remain; after two, a quarter; after three, an eighth; after four, a sixteenth.
The number of half-lives elapsed is the total time divided by the half-life, and counting the halvings on paper is more reliable than attempting a formula.
Questions often ask for the fraction remaining, the fraction decayed, or the time required to fall to a stated level. The fraction decayed is one minus the fraction remaining, and candidates frequently give one when the other was asked for.
On a graph of count rate against time, the half-life is found by taking the initial count rate, halving it, reading across to the curve and down to the time axis. Marks are given for showing these construction lines.
Half-lives vary enormously between isotopes, from fractions of a second to billions of years, and the choice of isotope for any application depends on matching the half-life to the task.
Background radiation
Background radiation is always present and must be subtracted from a measured count rate before the activity of a source is calculated. Failing to do so is a standard error.
Natural sources include radon gas seeping from rocks and soil, which is usually the largest contributor, cosmic rays from space, rocks and building materials, and radioactive isotopes naturally present in food and in the body.
Artificial sources include medical procedures such as X-rays and radiotherapy, nuclear waste, and fallout from past weapons testing.
Hazards, safety and detection
Radiation is hazardous because it ionises atoms in living cells. Lower doses can damage cells and cause mutations that may lead to cancer; higher doses can kill cells and cause radiation sickness.
Irradiation means exposing an object to radiation from an external source. The object does not become radioactive, and the exposure ends as soon as the source is removed or shielded. It is reduced by increasing distance, using shielding, and limiting the time of exposure.
Contamination means radioactive material has got onto or into an object, so the contaminating atoms continue to decay wherever they are. It is far harder to deal with, and is reduced by wearing gloves, using tongs, and sealing sources.
The difference is worth stating plainly: irradiation stops when the source is removed, while contamination persists until the radioactive material is physically removed.
Radiation is detected using a Geiger-Müller tube connected to a counter, or by photographic film, which is the basis of the film badges worn by workers to monitor their cumulative exposure.
Uses of radioactivity
Medical uses include treating cancer with gamma rays, using tracers to study organ function, and sterilising surgical instruments without heating them.
Industrial uses include checking the thickness of sheet material, where the count rate rises if the sheet becomes too thin; detecting leaks in underground pipes using a tracer; and sterilising food to extend shelf life.
Carbon dating estimates the age of once-living material from the proportion of carbon-14 remaining, since the isotope decays with a known half-life after the organism dies. The same principle applied to uranium isotopes dates rocks.
Smoke detectors use a weak alpha source that ionises air, allowing a small current to flow. Smoke absorbs the alpha particles, the current falls, and the alarm sounds.
The choice of source for each application follows from penetration and half-life. A thickness gauge needs beta, since alpha would be stopped entirely by the sheet and gamma would pass through unaffected regardless of thickness.
Fission and fusion
Nuclear fission is the splitting of a large unstable nucleus, such as uranium-235, into two smaller nuclei, releasing energy and two or three neutrons. Those neutrons can cause further fissions, producing a chain reaction.
In a nuclear reactor the chain reaction is controlled. Control rods absorb excess neutrons to keep the reaction steady, and a moderator slows the neutrons so that they are more likely to cause further fission. The energy released heats water to produce steam, which drives turbines to generate electricity.
Nuclear fusion is the joining of two small nuclei, such as isotopes of hydrogen, to form a larger nucleus, releasing far more energy per unit mass than fission. Fusion is the process powering the Sun and other stars.
Fusion requires extremely high temperatures and pressures so that the nuclei have enough energy to overcome their mutual electrostatic repulsion, which is why it has proved so difficult to achieve as a controlled power source on Earth.
Worked examples
Example 1: Completing a decay (3 marks)
A nucleus with mass number 226 and atomic number 88 emits an alpha particle. State the mass number and atomic number of the nucleus produced, and explain the changes.
An alpha particle consists of two protons and two neutrons, so four nucleons leave the nucleus and two of them are protons.
The mass number decreases by 4, giving 226 − 4 = 222. The atomic number decreases by 2, giving 88 − 2 = 86.
Because the atomic number has changed, the nucleus is now a different element.
Example 2: A half-life calculation (4 marks)
A sample has a count rate of 640 counts per second. Its half-life is 15 minutes. Calculate the count rate after 1 hour, and state the fraction of the original sample that has decayed.
One hour is 60 minutes, so the number of half-lives is 60 ÷ 15 = 4.
Halving four times: 640 becomes 320, then 160, then 80, then 40. The count rate after 1 hour is 40 counts per second.
The fraction remaining is one sixteenth, so the fraction that has decayed is 1 − 1/16 = 15/16, which is 93.75 per cent of the original sample.
Example 3: Choosing a source (4 marks)
A factory rolls aluminium sheet and needs to monitor its thickness continuously. Explain which type of radiation should be used.
Beta radiation should be used. Alpha particles would be completely absorbed by the aluminium sheet regardless of its thickness, so the count rate would always be near zero and would give no information about the thickness.
Gamma rays would pass almost entirely through the sheet whatever its thickness, so again the count rate would barely change and small variations would not be detected.
Beta particles are partly absorbed by a few millimetres of aluminium, so the count rate reaching the detector changes measurably with thickness. If the sheet becomes too thin, more beta particles pass through and the count rate rises, which can be used to adjust the rollers automatically. A source with a long half-life should be chosen so that the output does not fall noticeably during use.
Common mistakes and how to avoid them
The most damaging confusion in this topic is between contamination and irradiation. Irradiated objects do not become radioactive; contaminated objects carry the radioactive atoms with them.
Students often state that alpha radiation is the most dangerous without qualifying it. Alpha is the most ionising and is therefore very dangerous inside the body, but it is stopped by skin or paper, so it is far less hazardous from outside.
In nuclear equations, many candidates change the mass number during beta decay. It is unchanged, because a neutron becomes a proton and the total nucleon count stays the same.
Another frequent slip is forgetting to subtract background radiation before calculating the activity of a source.
Candidates often give the fraction remaining when the fraction decayed was requested. Read the final line of the question carefully.
Finally, many answers describe decay as happening at regular intervals or claim a particular nucleus is due to decay. Decay is entirely random, and half-life is a statistical average.
Exam technique for "Atomic and Nuclear Physics"
For half-life calculations, write out the successive halvings on paper rather than attempting them mentally. The sequence is checkable and takes seconds.
When reading half-life from a graph, draw the construction lines from the halved count rate across to the curve and down to the time axis, and leave them visible. Marks are awarded for the construction.
For questions on choosing a source, reason from penetration first and half-life second. If the radiation must pass through something, use gamma or beta; if it must be absorbed, use alpha.
In nuclear equation questions, check that the mass numbers balance and then that the atomic numbers balance, as two separate checks.
Always state that decay is random and spontaneous when explaining why predictions about individual nuclei cannot be made — it is frequently worth a mark of its own.
Quick revision summary
An atom has a tiny dense positive nucleus of protons and neutrons holding nearly all the mass, surrounded by electrons, with the atomic number identifying the element and the mass number giving total nucleons. Alpha scattering established this model: most particles passed through showing empty space, a few deflected showing concentrated positive charge, and a very few rebounded showing a small massive nucleus. Decay is spontaneous and random. Alpha is a helium nucleus, most ionising and least penetrating, stopped by paper; beta is a fast electron from a neutron becoming a proton, stopped by a few millimetres of aluminium; gamma is electromagnetic radiation, least ionising and most penetrating, needing lead or concrete, and undeflected by fields. Alpha decay reduces mass number by 4 and atomic number by 2, beta leaves mass number unchanged and raises atomic number by 1, gamma changes neither. Half-life is the time for the count rate or number of undecayed nuclei to halve, found by repeated halving or from a graph, and background radiation must be subtracted first. Irradiation stops when the source is removed while contamination persists. Fission splits a large nucleus releasing neutrons for a chain reaction controlled by rods and a moderator; fusion joins small nuclei, powers the Sun, and needs extreme temperature and pressure.