From Rutherford's gold foil to nuclear reactors: atoms, isotopes, radioactive decay, half-life, fission and fusion, explained with diagrams, animations and worked examples.
Everything you can touch, from a pencil to a planet, is made of atoms, and at the centre of every atom lies a nucleus about a hundred thousand times smaller than the atom itself. Some nuclei are unstable and break apart by themselves, releasing invisible radiation. That radiation can damage living cells, but it can also image a broken bone, treat cancer, date an ancient skeleton and light millions of homes. This article follows the story from the first discovery of the electron to the nuclear reactors of today. It explains what atoms are made of, what radioactivity is, how half-life works, where nuclear energy comes from, and how to stay safe.
The idea that matter is made of tiny indivisible particles goes back to ancient Greece, where the word atomos (uncuttable) was first used. The modern atomic theory began with the English chemist John Dalton in 1803. We now know that atoms can be divided: each is made of three kinds of subatomic particles.
| Particle | Charge | Relative mass | Where it is |
|---|---|---|---|
| Proton | +1 (+1.602 × 10⁻¹⁹ C) | 1 | In the nucleus |
| Neutron | 0 | 1 | In the nucleus |
| Electron | −1 (−1.602 × 10⁻¹⁹ C) | about 1/1840 | Around the nucleus, in shells |
The protons and neutrons together are called nucleons. The nucleus holds almost all of the atom's mass but occupies only a tiny volume, about 10⁻¹⁵ m across, while the whole atom is about 10⁻¹⁰ m across. A neutral atom has equal numbers of protons and electrons, so the positive and negative charges cancel. The electrons are arranged in energy levels called shells, and the way they are arranged decides the atom's chemistry.
The nucleus has a diameter of about 10⁻¹⁵ m and the atom about 10⁻¹⁰ m. If the nucleus were enlarged to the size of a pea (7 mm), how wide would the atom be?
Step 1. Ratio of diameters = 10⁻¹⁰ ÷ 10⁻¹⁵ = 10⁵ (100 000 times).
Step 2. Atom diameter = 7 mm × 10⁵ = 700 000 mm = 700 m, roughly the length of several football pitches.
Almost all of an atom is empty space, with the electrons somewhere in it. Solid objects feel solid because of the electric forces between the electron clouds of their atoms, not because the atoms are filled with matter.
In 1897 J. J. Thomson discovered the electron and proposed the "plum pudding" model, in which negative electrons were scattered through a ball of positive charge. In 1909 Hans Geiger and Ernest Marsden, working in Ernest Rutherford's laboratory in Manchester, fired alpha particles (fast, positively charged particles from a radioactive source) at a very thin sheet of gold foil, and counted how many were deflected.
The results shocked the experimenters:
In 1911 Rutherford explained these observations: the positive charge and nearly all the mass are packed into a tiny nucleus. The few alpha particles that happened to be aimed close to a nucleus were strongly repelled (positive charges repel). In 1913 Niels Bohr improved the model by placing the electrons in fixed energy levels. In 1932 James Chadwick discovered the neutron, completing the picture of the nucleus.
A nuclide is written with A and Z beside the chemical symbol, for example carbon-12 has A = 12 and Z = 6. Isotopes are atoms of the same element (same Z) with different numbers of neutrons (different A). They have the same chemical behaviour but different masses, and some are radioactive.
| Element | Isotope | Protons | Neutrons | Notes |
|---|---|---|---|---|
| Hydrogen | hydrogen-1 | 1 | 0 | The common form, one proton |
| Hydrogen | hydrogen-2 (deuterium) | 1 | 1 | Stable; used in fusion research |
| Hydrogen | hydrogen-3 (tritium) | 1 | 2 | Radioactive |
| Carbon | carbon-12 | 6 | 6 | Most common (about 99%) |
| Carbon | carbon-14 | 6 | 8 | Radioactive; used in dating |
| Uranium | uranium-235 | 92 | 143 | Fissile, used as fuel |
| Uranium | uranium-238 | 92 | 146 | Most of natural uranium |
(a) How many protons, neutrons and electrons are in a neutral atom of potassium-39 (Z = 19)? (b) Chlorine occurs naturally as about 75% chlorine-35 and 25% chlorine-37. Find the average relative atomic mass.
(a) Protons = Z = 19. Neutrons = A − Z = 39 − 19 = 20. Electrons = 19 (neutral atom).
(b) Average = (0.75 × 35) + (0.25 × 37) = 26.25 + 9.25 = 35.5, which is the value printed on the periodic table.
The forces inside a nucleus must hold the protons together against their mutual electric repulsion. Some nuclei, with too many neutrons, too few, or simply too many particles, are unstable. They decay by emitting radiation and become a more stable nucleus. This is radioactivity, and it was discovered by the French physicist Henri Becquerel in 1896 when uranium salts fogged photographic plates. Marie and Pierre Curie soon found the new radioactive elements polonium and radium (1898), and in 1899 Rutherford showed that the radiation had at least two types, which he called alpha and beta. Gamma was identified shortly afterwards.
Radioactive decay has four key properties:
The activity of a source is the number of nuclei that decay each second. The unit is the becquerel (Bq): 1 Bq = 1 decay per second. In experiments we measure the count rate, the number of detected particles per minute or second.
Background radiation is the low level of radiation that is always present. Its main natural sources are radon gas from rocks and soil, cosmic rays from space, rocks and building materials, and traces of radioactive elements such as potassium-40 in food and in our own bodies. Man-made sources include medical X-rays. The average natural background dose worldwide is about 2.4 millisieverts (mSv) a year according to the UN scientific committee on radiation (UNSCEAR), though it varies a lot from place to place. When measuring a source, always subtract the background count from the readings.
Detectors. A Geiger–Müller tube clicks or counts each time radiation ionises the gas inside it. Photographic film (used in badges) darkens when exposed. A cloud chamber shows the tracks of particles as tiny trails of droplets. Scintillation counters convert radiation to flashes of light.
| Alpha (α) | Beta-minus (β⁻) | Gamma (γ) | |
|---|---|---|---|
| What it is | A helium nucleus: 2 protons + 2 neutrons | A fast electron from the nucleus | High-energy electromagnetic wave (photon) |
| Charge | +2 | −1 | 0 |
| Relative mass | 4 | about 1/1840 | 0 |
| Ionising power | Very strong | Moderate | Weak |
| Penetration | Stopped by paper or a few cm of air | Stopped by a few mm of aluminium | Reduced by thick lead or concrete; never completely stopped |
| Deflection by a magnetic or electric field | Small, towards the negative side | Large, in the opposite direction | None |
Because alpha particles are so strongly ionising and cannot get through skin or even paper, an alpha source outside the body is relatively harmless, but one that is swallowed, inhaled or inside the body (such as radon gas or polonium) is very dangerous because it delivers all its energy to nearby cells. Gamma rays are the most penetrating, so they are the main hazard from a source outside the body.
When a nucleus decays it changes into another nucleus. In writing the decay we must keep two things equal on both sides: the total nucleon number (A) and the total charge (Z).
Americium-241 (Z = 95), used in smoke detectors, decays by alpha emission. Write the equation.
Daughter nucleus: A = 241 − 4 = 237, Z = 95 − 2 = 93. Element 93 is neptunium (Np).
Am-241 → Np-237 + He-4. Check: 241 = 237 + 4 ✓ and 95 = 93 + 2 ✓.
Cobalt-60 (Z = 27) decays by beta-minus emission to an isotope of nickel (Z = 28). Write the equation.
A stays 60 and Z rises to 28: Co-60 → Ni-60 + e⁻ + antineutrino. Check charge: 27 = 28 + (−1) ✓.
The nickel nucleus is left in an excited state and sheds energy by emitting two gamma rays (of about 1.17 and 1.33 MeV). These gamma rays are why cobalt-60 is used in radiotherapy and sterilisation.
Uranium-238 (Z = 92) emits an alpha particle, giving thorium-234, which emits a beta-minus particle. Find the nucleus produced.
Alpha: Z = 92 − 2 = 90 (thorium), A = 238 − 4 = 234.
Beta-minus from Th-234: A stays 234, Z = 90 + 1 = 91 (protactinium). Result: Pa-234.
The process continues through a long series of decays and ends at stable lead-206.
Since decay is random, we cannot say when a particular nucleus will decay, but we can say how long it takes for half of a large sample to decay. The half-life (T½) of an isotope is the time taken for half of the radioactive nuclei in a sample to decay, which is also the time for the activity (and the count rate) to fall to half. After each half-life, half of what remained decays again, so the amount follows a repeating-halving pattern:
N = N₀ × (½)ⁿ where n = t ÷ T½ is the number of half-lives that have passed.
The same formula applies to activity A and count rate. The half-life of a given isotope is a fixed property, unaffected by temperature, pressure or chemical state.
A sample of 80 g of a radioisotope with a half-life of 6.0 hours is left for 24 hours. How much remains?
Step 1. n = 24 ÷ 6.0 = 4 half-lives.
Step 2. 80 → 40 → 20 → 10 → 5. Or N = 80 × (½)⁴ = 80 ÷ 16 = 5.0 g.
A student measures 420 counts per minute from a source and 20 counts per minute with the source removed. The half-life is 5.0 min. What count rate will she measure after 15 minutes?
Step 1. Corrected count rate = 420 − 20 = 400 counts/min.
Step 2. n = 15 ÷ 5.0 = 3 half-lives, so corrected rate = 400 × (½)³ = 50 counts/min.
Step 3. The detector will read 50 + 20 = 70 counts/min, because the background is still there.
| Isotope | Half-life (approximate) | Use or comment |
|---|---|---|
| Polonium-212 | 0.3 microseconds | Extremely short-lived |
| Technetium-99m | 6 hours | Medical imaging |
| Iodine-131 | 8 days | Thyroid treatment |
| Radon-222 | 3.8 days | Natural radioactive gas |
| Cobalt-60 | 5.3 years | Radiotherapy, sterilisation |
| Caesium-137 | 30 years | Industrial gauges; nuclear waste |
| Carbon-14 | 5730 years | Radiocarbon dating |
| Plutonium-239 | 24 000 years | Nuclear fuel and waste |
| Uranium-238 | 4.5 billion years | Natural uranium; dating rocks |
Radiocarbon dating. Cosmic rays constantly make carbon-14 in the upper atmosphere, and living plants and animals take it in, so the fraction of carbon-14 in living things stays constant. When an organism dies it stops taking in carbon, and the carbon-14 already in it decays with a half-life of 5730 years. By measuring how much is left, we can estimate how long ago it died. For example, a wooden tool with a quarter of the carbon-14 of living wood has passed through two half-lives, so it is about 2 × 5730 = 11 460 years old. The method works to about 50 000 years, and the results are calibrated against other records such as tree rings.
The probability per second that a given nucleus decays is the decay constant λ. The activity is A = λN and the half-life is T½ = ln 2 ÷ λ = 0.693 ÷ λ. For carbon-14, λ = 0.693 ÷ 5730 years ≈ 1.2 × 10⁻⁴ per year.
Ionising radiation can break chemical bonds and damage DNA. Large doses can cause radiation sickness, burns and cancer; small doses carry a small increase in the risk of cancer later. The effect on the body is measured in sieverts (Sv), but since a sievert is large, we use millisieverts (mSv), where 1 mSv = 0.001 Sv. Some typical values are given below (approximate and variable).
| Source of dose | Approximate dose |
|---|---|
| Chest X-ray | 0.02–0.1 mSv |
| Natural background (world average, per year) | about 2.4 mSv |
| CT scan of the head | about 2 mSv |
| Recommended limit for the public from artificial sources (per year) | 1 mSv |
| Recommended limit for radiation workers (averaged over 5 years) | 20 mSv per year |
Limits are set by international bodies such as the International Commission on Radiological Protection (ICRP). Medical exposures are justified when the benefit to the patient is clearly greater than the small risk. Radiation workers protect themselves with three rules:
In addition, sources are handled with tongs, stored in labelled lead-lined containers, never pointed at people, and workers wear film badges or electronic dosimeters. Unsealed sources are handled with gloves and a ban on eating or drinking in the area to prevent contamination. Note the difference between irradiation (being exposed to radiation from a source outside the body, which does not make you radioactive) and contamination (having radioactive material on or in your body).
If you weigh a helium-4 nucleus carefully, its mass is slightly less than the total mass of the two protons and two neutrons separately. The missing mass is the mass defect. It has not vanished: in 1905 Einstein showed that mass and energy are equivalent, with E = mc², where c is the speed of light. The mass defect corresponds to the energy that was released when the nucleons joined, and the same amount of energy is needed to pull them apart again. It is called the binding energy.
Masses in atomic mass units (u): proton 1.007276, neutron 1.008665, helium-4 nucleus 4.001506. Find the binding energy (1 u is equivalent to 931.5 MeV).
Step 1. Separate nucleons: 2 × 1.007276 + 2 × 1.008665 = 2.014552 + 2.017330 = 4.031882 u.
Step 2. Mass defect = 4.031882 − 4.001506 = 0.030376 u.
Step 3. Binding energy = 0.030376 × 931.5 ≈ 28.3 MeV, or about 7.1 MeV per nucleon.
A graph of binding energy per nucleon against nucleon number explains why both fission and fusion release energy. Nuclei near iron-56 are the most tightly bound.
Nuclear fission is the splitting of a large nucleus into two smaller ones. It was discovered in 1938 by the German chemists Otto Hahn and Fritz Strassmann, and explained in early 1939 by Lise Meitner and Otto Frisch. When a slow neutron strikes a uranium-235 nucleus, the nucleus absorbs it, becomes unstable, and splits, releasing about 200 MeV of energy as kinetic energy of the fragments, plus two or three more neutrons. A typical reaction is:
U-235 + n → Ba-141 + Kr-92 + 3 n + energy (check: 235 + 1 = 141 + 92 + 3 ✓ and 92 = 56 + 36 ✓)
Because each fission releases up to three neutrons, each of which can cause another fission, a chain reaction can build up. In a bomb, the chain reaction is allowed to grow uncontrolled. In a nuclear reactor it is carefully controlled so that, on average, exactly one neutron from each fission causes another fission. The first controlled chain reaction was achieved by Enrico Fermi's team at Chicago on 2 December 1942.
Estimate the energy released if all of the uranium-235 in 1.0 kg fissions, at 200 MeV per fission. (Take 1 MeV = 1.6 × 10⁻¹³ J and 235 g of U-235 contains 6.0 × 10²³ atoms.)
Step 1. Atoms = (1000 ÷ 235) × 6.0 × 10²³ ≈ 2.6 × 10²⁴.
Step 2. Energy per fission = 200 × 1.6 × 10⁻¹³ = 3.2 × 10⁻¹¹ J.
Step 3. Total energy = 2.6 × 10²⁴ × 3.2 × 10⁻¹¹ ≈ 8 × 10¹³ J (about 80 TJ).
Burning 1 kg of coal releases about 3 × 10⁷ J, so the fission of 1 kg of uranium-235 gives roughly three million times more energy. (In practice reactor fuel contains only a few per cent U-235, and not all of it is used.)
A typical nuclear power station uses the energy of fission to boil water, and the steam drives a turbine and generator, just as in the thermal power station described in the article on energy. The main parts of a reactor are:
The first nuclear power station to supply electricity to a grid was at Obninsk in the USSR in 1954. In Pakistan, the Karachi Nuclear Power Plant (KANUPP) started operating in 1972, and the Pakistan Atomic Energy Commission now operates several nuclear plants at Karachi and Chashma. Nuclear power stations produce almost no carbon dioxide while operating and generate large amounts of reliable electricity from small amounts of fuel. On the other hand, they produce radioactive waste, some of which stays dangerous for thousands of years; they are costly to build; and serious accidents, although rare, can have major consequences (Three Mile Island 1979, Chernobyl 1986 and Fukushima 2011). Spent fuel is stored first in cooling pools and then in sealed dry casks, and many countries plan deep underground repositories for the most hazardous waste. Whether and how to use nuclear power involves weighing these benefits and risks, together with cost, safety and alternatives such as solar, wind and hydropower.
Nuclear fusion is the joining of two light nuclei to form a heavier one, releasing energy. It is what powers the Sun and other stars. Inside the Sun, hydrogen nuclei fuse step by step into helium, converting about 4 million tonnes of mass into energy every second. On Earth, the most promising reaction joins two hydrogen isotopes:
H-2 + H-3 → He-4 + n + 17.6 MeV
Fusion fuel is plentiful (deuterium comes from seawater), and fusion produces no long-lived high-level waste of the kind from fission, but it is very hard to achieve. Nuclei repel each other, so they must be heated to over a hundred million degrees Celsius and held together long enough, usually inside a ring of strong magnetic fields (as in the international ITER project under construction in France) or by compressing tiny fuel pellets with lasers. In December 2022 the National Ignition Facility in the United States reported a laser-driven fusion shot that released more energy than the laser energy delivered to the target, a scientific milestone; a power plant that continuously produces more electricity than it uses has not yet been built.
Protons and neutrons are not the end of the story. In the 1960s physicists showed that they are made of smaller particles called quarks. A proton contains two "up" quarks and one "down" quark (uud); a neutron contains one up and two down (udd). Electrons are not made of anything smaller, as far as we know; they belong to a family called leptons. Each particle has an antiparticle with the same mass and opposite charge. The positron (antielectron) was discovered by Carl Anderson in 1932. The Standard Model of particle physics organises the known particles and three of the four fundamental forces, and it was strongly confirmed by the discovery of the Higgs boson at CERN in 2012. Gravity is not included, and the nature of dark matter is still unknown.
Try each question before opening the answer.
Protons = 11. Neutrons = 23 − 11 = 12. Electrons = 11.
Most of the atom is empty space; the positive nucleus occupies only a tiny volume, so most alpha particles never came near a nucleus.
Alpha is stopped by paper. Beta passes through paper but is stopped by a few millimetres of aluminium.
A = 226 − 4 = 222; Z = 88 − 2 = 86 (radon). Ra-226 → Rn-222 + He-4.
A = 14, Z = 7, which is nitrogen: C-14 → N-14 + e⁻ + antineutrino.
30 ÷ 10 = 3 half-lives. 1600 → 800 → 400 → 200 Bq.
12.5% = (½)³, so 3 half-lives: 3 × 5730 = 17 190 years.
Control rods absorb neutrons to control (or stop) the chain reaction. The moderator slows neutrons so they are more likely to cause fission in uranium-235.
Real radioactive sources need trained supervision and are restricted in many schools, but you can model radioactive decay safely with 100 dice or coins: roll all the dice, remove those that show a six (or the heads), count those left, and repeat; the graph of the number remaining against the number of rolls looks just like a decay curve, and it shows that decay is random yet predictable. You can also use a free simulation of the Rutherford experiment, use a cloud chamber demonstration, discuss the uses and risks of radiation with a local hospital or university department, and explore the distribution of background radiation with a Geiger counter if one is available. Numerical values are rounded; please check that they match the data booklet used by your examination board.
This article is original EDUSAMBAM writing. Definitions, data and historical facts were checked against the sources below. Diagrams are original and were not copied from any source.
Note on the numbers: doses, half-lives and masses are rounded standard values. Nuclear statistics and the status of fusion research change over time, so check current data from the IAEA and national agencies. Please check numerical values against your own syllabus or exam board specification before relying on them.
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