Particle Physics

Evidence for the nuclear atom: the alpha-particle scattering experiment

Before 1911 the accepted picture of the atom was a sphere of positive charge with electrons buried inside it. Geiger and Marsden, working in Rutherford's laboratory between 1909 and 1911, tested that picture. They fired a narrow beam of alpha particles from a radioactive source at a very thin gold foil - about 400 nm thick, a few thousand atoms deep - inside an evacuated chamber. Around the foil they placed a screen coated with zinc sulphide, which gives a tiny flash of light, a scintillation, when an alpha particle strikes it, and they counted the flashes with a microscope that could be moved to any angle.

The results were not what the old model predicted. Almost every alpha particle passed straight through the foil, losing hardly any energy and being deflected by less than a degree or two. A small number were deflected through moderate angles, and roughly 1 alpha particle in 8000 was deflected through more than 90 degrees, so that it came back towards the source. An alpha particle is a helium nucleus, with a mass about 7000 times that of an electron and a charge of +2e, travelling at about 1.5 x 10^7 m s-1, so something both massive and strongly charged had to be turning it round.

Each observation pins down one feature of the atom. Because the great majority of alpha particles pass straight through, with almost no deflection, the atom must be mostly empty space: the orbiting electrons are far too light to deflect a fast alpha particle appreciably by electrostatic repulsion. Because a small fraction are deflected through large angles, the atom must contain a region of concentrated positive charge, since only a force of electrostatic repulsion from a large positive charge can turn a positive alpha particle back. Because such large deflections are so rare, that region must be very small compared with the atom: the chance of a head-on approach is tiny. And because the alpha particles bounce back rather than being pushed aside, that region must contain nearly all the mass of the atom, and must be the same for every element.

The model that follows is the nuclear atom: a tiny, dense, positively charged nucleus made of protons and neutrons, surrounded by much lighter negative electrons in the space outside it. The numbers are worth remembering, because they explain the rarity of the large deflections. An atom is about 10-10 m across, while a nucleus is only about 10-15 m to 10-14 m across, so the nucleus is roughly 10000 times smaller than the atom. Scaled up, an atom would be a football stadium and its nucleus a pea on the centre spot - which is why an alpha particle usually misses every nucleus in its path and sails straight through.

• Most alpha particles pass straight through the foil: the atom is mostly empty space.
• A few are deflected through large angles: the atom contains a concentrated positive charge, which repels the positive alpha particles.
• The large deflections are very rare (about 1 in 8000): the nucleus is very small compared with the whole atom.
• Alpha particles bounce back rather than being pushed aside: the nucleus contains nearly all the mass of the atom.

Nucleon number, proton number, isotopes and the unified atomic mass unit

The nucleus contains nucleons: positively charged protons and neutral neutrons. The proton number Z is the number of protons in a nucleus, and it is also the number of electrons in a neutral atom, so it fixes both the element and its chemical behaviour. The nucleon number A is the total number of protons and neutrons, so the number of neutrons is A - Z. Two atoms with the same proton number are the same element, and can differ only in how many neutrons they carry.

Isotopes are forms of the same element with different numbers of neutrons in their nuclei, so they have the same proton number but different nucleon numbers. Hydrogen has three: hydrogen-1 (1 proton, 0 neutrons), deuterium (1 proton, 1 neutron) and tritium (1 proton, 2 neutrons). Because all three have one proton and one electron, they react chemically in exactly the same way, but tritium is radioactive while hydrogen-1 and deuterium are stable. Carbon-12 and carbon-14 likewise both have 6 protons and 6 electrons, but carbon-14 has 8 neutrons and is unstable.

A particular nuclear species, called a nuclide, is written with the nucleon number above the proton number in front of the chemical symbol: uranium-238 is written as 238/92 U, where 238 is the nucleon number and 92 the proton number. You will find both forms used, 238/92 U and U-238, and you must be able to read either and work out the numbers from the other. Uranium-238 has 238 - 92 = 146 neutrons, and if it is named uranium the proton number must be 92, because that is what makes an atom uranium.

The unified atomic mass unit, u, is defined as one twelfth of the mass of a single atom of carbon-12, and 1 u = 1.66 x 10-27 kg. It is used because the masses involved are so small that kilograms give unwieldy numbers, and because the value in u depends only weakly on the nuclide: a nucleon has a mass of very nearly 1 u. Through E = mc^2, 1 u of mass is equivalent to about 931 MeV of energy, which is why masses in u can be turned directly into the energies released in nuclear reactions. The mass of an electron is only 9.11 x 10-31 kg, or 0.00055 u, so an atom's mass is almost entirely in its nucleus.

Nucleon number and charge are conserved in nuclear processes

In any nuclear process - a radioactive decay, a collision, an absorption of a neutron - nucleon number and charge are conserved. Add up the nucleon numbers on the left of the equation and on the right, and the two totals must be equal, because nucleons are neither created nor destroyed. Add up the proton numbers in the same way, and the totals must again be equal, because the total positive charge of the nuclei is conserved; radiation that is emitted carries its own charge away with it. Energy and momentum are conserved too, which is what forces the nuclear products to share the energy released.

Alpha decay. The nucleus emits an alpha particle, which is a helium nucleus: 2 protons and 2 neutrons, nucleon number 4 and proton number 2. So the nucleon number falls by 4 and the proton number falls by 2. Uranium-238, for example, decays to thorium-234 by emitting an alpha particle: 238 = 234 + 4, and 92 = 90 + 2, so both totals balance. Because the proton number changes, the product is a different element.

Beta decay. A beta particle has nucleon number 0 and a charge of -1e (beta-minus) or +1e (beta-plus). In beta-minus decay the nucleon number is unchanged and the proton number rises by 1, and in beta-plus decay the nucleon number is unchanged and the proton number falls by 1. Carbon-14 decays by beta-minus emission to nitrogen-14: 14 = 14 + 0, and 6 = 7 - 1. Gamma emission changes neither number, because a gamma photon carries no nucleons and no charge; the nucleus simply loses energy.

A beta decay equation is not complete without the (anti)neutrino, and its mass and charge are both zero, so adding it leaves both totals unchanged: 14/6 C -> 14/7 N + 0/-1 beta particle + antineutrino. Sodium-22 decays by beta-plus emission to neon-22: 22/11 Na -> 22/10 Ne + 0/+1 beta particle + neutrino, with 22 = 22 + 0 and 11 = 10 + 1. Write the symbol in the form 0/-1 for a beta-minus particle and 0/+1 for a positron, so that the charge balance is visible.

Alpha, beta-minus, beta-plus and gamma: composition, mass and charge

An alpha particle is a helium nucleus: 2 protons and 2 neutrons, so a mass of about 4.00 u (6.64 x 10-27 kg) and a charge of +2e. It is the heaviest and the slowest of the emissions, so it ionises the atoms it passes very strongly and gives up all its energy within a few centimetres of air or a sheet of paper.

A beta particle is a high-speed electron created in the nucleus and thrown out of it. Its mass is 9.11 x 10-31 kg, only about 1/1840 of the mass of a proton, and its charge is -1e. Because it is so light, and moves at up to almost the speed of light, it ionises much less strongly than an alpha particle but travels much further, being stopped by a few millimetres of aluminium.

A positron is the same particle with a positive charge: mass 9.11 x 10-31 kg, charge +1e. It is emitted in beta-plus decay, and it is the antiparticle of the electron. A positron behaves as a normal particle until it meets an electron, when the two annihilate each other and their combined mass appears as two gamma-ray photons travelling in opposite directions. Positrons are common in medical imaging, and they were first seen in 1932 by Carl Anderson in cloud-chamber photographs of cosmic rays, where the track curved in the wrong direction for an electron.

Gamma radiation is high-energy electromagnetic radiation: a photon with no charge and no rest mass, emitted when a nucleus that has surplus energy settles to a lower energy state. It ionises very weakly but penetrates very strongly, and several centimetres of lead are needed to absorb a useful fraction of it. Learn the direction of each order, because the two are opposite: alpha is the most ionising and the least penetrating, gamma the least ionising and the most penetrating, and beta lies between them.

Neutrinos, antineutrinos and the continuous beta energy spectrum

Look at the energies of the particles emitted by one source and an important difference appears. Alpha particles from a given decay come out with one of a few sharply defined energies, because the same two particles - the alpha particle and the daughter nucleus - are produced every time, and the fixed amount of energy released is always divided between them in the same proportions. The alpha spectrum is discrete.

The beta spectrum is not. Beta particles from a single source come out with every energy from nearly zero up to a maximum, spread over a continuous range. At first this looked as though energy was not conserved in beta decay, and some physicists were prepared to give up the idea. In 1930 Pauli suggested that a second, invisible particle is emitted at the same time and carries away the missing energy.

That particle is the neutrino: neutral, almost massless, and interacting so weakly that it passes through the whole Earth without being stopped. It is produced in beta-plus decay, where the nucleus emits a positron, and its antiparticle, the antineutrino, is produced in beta-minus decay. In beta decay the energy released is shared between the beta particle and the (anti)neutrino, and the way it is shared is different in every decay, so a beta particle can be detected with any energy up to the maximum value, which is the total energy released.

The (anti)neutrinos are real and are detected on an enormous scale. Nuclear reactors are the most intense artificial source, because every beta decay in the fission products produces an antineutrino; Cowan and Reines detected reactor antineutrinos in 1956, confirming Pauli's idea and the conservation of energy. The Sun produces them in the fusion reactions of its core, and detectors such as the Sudbury Neutrino Observatory in Canada use a thousand tonnes of heavy water to catch a handful of them each day. Beta decay is also the reason the beta spectrum must end at the maximum energy: a beta particle cannot carry more than the whole energy released, because there is nothing left to give.

• Alpha particles have discrete energies: the same particles are produced in every decay, so the energy released is always shared in the same way.
• Beta particles have a continuous range of energies: the energy is shared between the beta particle and an (anti)neutrino, and the split varies from decay to decay.
• Beta-minus decay emits an electron antineutrino; beta-plus decay emits an electron neutrino.
• The maximum beta energy is the total energy released, when the (anti)neutrino carries almost none of it.

Quarks: six flavours, baryons and mesons

Not all particles are fundamental: a proton and a neutron are both built from smaller particles called quarks, so they are not fundamental. There are six flavours of quark - up, down, strange, charm, top and bottom - and the only property you need is charge. An up, charm or top quark carries a charge of +2/3 e; a down, strange or bottom quark carries a charge of -1/3 e. Quarks have never been observed on their own; they are always found in groups inside larger particles.

Protons and neutrons are made of three quarks each. A proton is up, up, down (uud), and its charge is (+2/3) + (+2/3) + (-1/3) = +1e. A neutron is up, down, down (udd), and its charge is (+2/3) + (-1/3) + (-1/3) = 0. The quark charges are fractional, but the charges that are published in tables are always whole multiples of e, because bound quarks only ever appear in combinations that add up to a whole number of electronic charges.

Every quark has an antiquark with the opposite charge: the antiquark of an up quark carries a charge of -2/3 e, and the antiquark of a down quark carries +1/3 e. A particle made of quarks is called a hadron, and hadrons come in exactly two kinds. A baryon consists of three quarks, and the proton and the neutron are the baryons you know best. A meson consists of one quark and one antiquark, so the positive pion, written pi+, is an up quark together with an anti-down quark: (+2/3) + (+1/3) = +1e, and its antiparticle pi- is an anti-up quark with a down quark, charge -1e. Baryons and mesons are both hadrons, but they are distinguished by their quark structure, not by their mass or charge.

Leptons are the other family. An electron is a lepton, and so is a neutrino: both are fundamental particles, so neither is made of quarks. Leptons do not feel the strong interaction that holds the nucleus together, whereas hadrons do, and that is the deepest difference between the two families. The particles you must be able to classify are therefore: proton and neutron as baryons, pions and other quark-antiquark pairs as mesons, and electrons, positrons, neutrinos and antineutrinos as leptons. A positron is the antiparticle of an electron and an antineutrino is the antiparticle of a neutrino, but all of them are leptons.

Beta decay in terms of quarks

Because a neutron is udd and a proton is uud, the difference between them is a single quark flavour. In beta-minus decay one down quark changes into an up quark and the neutron becomes a proton: d -> u + beta-minus particle + antineutrino. On the left the charge is -1/3 e; on the right the up quark contributes +2/3 e and the electron contributes -1e, so +2/3 - 1 = -1/3 e, exactly the same. The quark has turned into another flavour of quark, the number of quarks - and therefore the nucleon number - is unchanged, and the charge lost by the quark appears as the charge of the emitted electron.

In beta-plus decay it is the other way round: one up quark changes into a down quark, so a proton becomes a neutron, and a positron and an electron neutrino are emitted along with it: u -> d + positron + neutrino. Again the charge balances: +2/3 e on the left, and -1/3 + 1 = +2/3 e on the right. Notice the pattern that examiners look for. A neutron carries one more down quark than a proton, so an excess of neutrons is corrected by beta-minus decay, and an excess of protons is corrected by beta-plus decay; in both cases the quark change moves the nucleus towards the line of stability.

The same idea explains why a free neutron is radioactive while a proton is not. A free neutron decays by beta-minus emission with a half-life of about 15 minutes, because a single neutron outside a nucleus is slightly heavier than a proton plus an electron, and the down quark in it can change into an up quark. Inside most stable nuclei the presence of the other nucleons makes it impossible, but in a nucleus with too many neutrons for its protons the decay proceeds, and the nucleus becomes a different element.

Finally, keep the scale in mind. The mass difference that drives a beta decay is equivalent to less than 1 MeV of energy, while the mass of a whole nucleon is about 939 MeV. The quark changes that release nuclear energy move the masses in the seventh significant figure, which is why the very large energies released by nuclear processes come from tiny changes in mass. The unified atomic mass unit is the natural unit for those changes: 1 u = 1.66 x 10-27 kg, equivalent to about 931 MeV.

• Beta-minus: a down quark becomes an up quark (d -> u), so a neutron becomes a proton; an electron and an electron antineutrino are emitted.
• Beta-plus: an up quark becomes a down quark (u -> d), so a proton becomes a neutron; a positron and an electron neutrino are emitted.
• In both decays the number of quarks is unchanged, so the nucleon number is unchanged.
• The charge of the emitted electron or positron is exactly the charge that the changed quark loses or gains.