Topic 5: E. Nuclear and quantum physics

This theme explores the tiny world inside the atom and the strange rules that govern it. You will see how the nucleus stores enormous energy, how unstable nuclei decay over time, and how light and matter behave as both particles and waves.

The nuclear model of the atom

Rutherford's gold foil experiment fired alpha particles at a thin metal sheet. Most passed straight through, but a few bounced back at large angles. This forced a rethink: the atom is mostly empty space, with nearly all its mass and all its positive charge packed into a tiny central nucleus. Electrons orbit this nucleus at relatively huge distances. A nucleus is built from protons and neutrons (collectively nucleons). The number of protons, the atomic number Z, fixes which element it is, while the total nucleon count is the mass number A. We write a nuclide as, for example, U-235, meaning uranium with A = 235. Atoms of the same element with different neutron numbers are isotopes; they share chemical behaviour but differ in mass and nuclear stability.

Atomic spectra and discrete energy levels

Electrons in an atom can only occupy certain fixed energy levels, not any value in between. When an electron drops from a higher level to a lower one, the atom emits a photon whose energy exactly equals the gap between the levels: E = hf, where h is the Planck constant. Because the gaps are discrete, only specific photon frequencies are released, producing a line spectrum of bright coloured lines unique to each element. Absorption works in reverse: an atom absorbs only photons that match an available jump upward, leaving dark lines in a continuous spectrum. These spectra are powerful evidence that energy inside atoms is quantized, and astronomers use them to identify the elements present in distant stars.

Radioactive decay: alpha, beta and gamma

Unstable nuclei shed energy by emitting radiation. Alpha decay releases a helium-4 nucleus (2 protons, 2 neutrons), reducing A by 4 and Z by 2; alpha particles are heavily ionizing but stopped by paper. Beta-minus decay converts a neutron into a proton, emitting an electron and an antineutrino, so Z rises by 1 while A is unchanged; beta particles penetrate further and are stopped by a few millimetres of aluminium. Gamma decay emits a high-energy photon as the nucleus settles to a lower energy state, changing neither A nor Z. A sample decay equation: Ra-226 -> Rn-222 + He-4 (alpha). For beta: C-14 -> N-14 + electron + antineutrino. In every decay equation, both nucleon number and charge must balance on each side.

Half-life and activity (worked example)

Radioactive decay is random for any single nucleus but predictable for large numbers. The half-life is the time for half the nuclei in a sample to decay. Activity, measured in becquerel (Bq, decays per second), is proportional to the number of undecayed nuclei, so it also halves every half-life. Worked example: a source has an initial activity of 800 Bq and a half-life of 3 hours. After 3 hours the activity is 400 Bq; after 6 hours, 200 Bq; after 9 hours, 100 Bq; after 12 hours, 50 Bq. So after four half-lives (12 hours) the activity has fallen to 800 / 2^4 = 50 Bq. The remaining fraction after n half-lives is always (1/2)^n.

Mass-energy equivalence and the unified atomic mass unit

Einstein showed that mass and energy are two forms of the same thing, linked by E = mc^2, where c is the speed of light. Because c^2 is enormous, even a tiny mass corresponds to a large energy. In nuclear physics we measure mass with the unified atomic mass unit (u), defined as one twelfth of the mass of a carbon-12 atom, equal to about 1.66 x 10^-27 kg. Conveniently, 1 u of mass is equivalent to about 931.5 MeV of energy. This lets us convert mass differences directly into the energy released or absorbed in a nuclear reaction, which is far too large to ignore compared with chemical reactions.

Nuclear binding energy and stability

The mass of a nucleus is always slightly less than the total mass of its separate protons and neutrons. This missing mass, the mass defect, has been converted into the binding energy that holds the nucleus together (using E = mc^2). To compare nuclei fairly we use the binding energy per nucleon: the higher this value, the more tightly bound and stable the nucleus. Plotting binding energy per nucleon against mass number gives a curve that rises steeply, peaks around iron-56 (the most stable nuclide), then slowly falls. This curve is the key to nuclear energy: moving toward the iron peak releases energy, which is why both fission of heavy nuclei and fusion of light nuclei can be energy sources.

Nuclear fission and fusion

Fission splits a heavy nucleus into two lighter ones. When U-235 absorbs a slow neutron it becomes unstable and breaks apart, releasing more neutrons and a large amount of energy. Those neutrons can trigger further fissions, producing a chain reaction that is controlled in nuclear reactors and uncontrolled in weapons. Fusion joins light nuclei into a heavier one, for example two hydrogen isotopes combining to form helium. Both processes release energy because the products have a higher binding energy per nucleon than the reactants, moving toward the iron-56 peak. Fusion releases more energy per nucleon than fission, but requires extreme temperatures and pressures to overcome the electrostatic repulsion between positive nuclei.

Fusion in stars and nucleosynthesis

Stars are giant fusion reactors. In the core of a star like the Sun, hydrogen nuclei fuse to form helium, releasing the energy that makes the star shine and creating an outward pressure that balances gravity. As a star ages and its core hydrogen runs low, it can fuse helium into heavier elements such as carbon and oxygen. Massive stars continue building elements up to iron through successive fusion stages. Because iron sits at the binding-energy peak, fusing beyond it absorbs rather than releases energy, so elements heavier than iron are forged in the violent conditions of supernova explosions. This stellar nucleosynthesis is the origin of most of the chemical elements around us.

The photoelectric effect and photons

Shining light on a metal surface can eject electrons, but only if the light's frequency is above a threshold value, no matter how bright the light. This puzzled classical wave theory and led Einstein to model light as packets called photons, each carrying energy E = hf. A single photon gives all its energy to one electron. The electron must first overcome the work function (the minimum energy to escape the metal); any leftover becomes the electron's maximum kinetic energy: E_max = hf - work function. Increasing intensity adds more photons, releasing more electrons, but does not raise their maximum kinetic energy. The photoelectric effect is strong evidence that light is quantized into particles.

Matter waves (HL)

If waves can behave like particles, de Broglie proposed that particles can behave like waves. Any moving object has an associated wavelength given by the de Broglie relation, wavelength = h / p, where p is the momentum. For everyday objects this wavelength is far too small to notice, but for electrons it is comparable to atomic spacings. This was confirmed when beams of electrons were diffracted by crystals, producing interference patterns just like light. Wave-particle duality means both light and matter show particle and wave properties depending on the experiment, a cornerstone of quantum physics. It also underpins the electron microscope, which uses the short wavelength of fast electrons to resolve tiny structures.