Nuclear and Particle Physics: Decay, Fission and Quarks

A nucleus is written with its mass number on top and its atomic number below, like ¹⁴₆C for carbon-14. The atomic number Z counts the protons, and the mass number A counts protons plus neutrons, so the number of neutrons is N = A − Z.

Every carbon atom has 6 protons, but the number of neutrons can vary. Carbon-12, with 6 neutrons, makes up about 99% of carbon. Carbon-14, with 8, is rare and radioactive. Isotopes of an element behave the same way in chemical reactions, because chemistry depends on electrons, but their nuclei can behave very differently.

A nucleus is about 10⁻¹⁵ m across, a femtometer, while a whole atom is about 10⁻¹⁰ m.

Protons repel each other, and inside a nucleus they're so close that the push is huge. What holds them together is the strong nuclear force. It attracts protons and neutrons to each other, and at distances of about a femtometer it's far stronger than the electric repulsion. But it fades to almost nothing beyond a few femtometers, so it only acts between close neighbors. Neutrons add attraction without adding repulsion, which is why heavy nuclei need more neutrons than protons.

Here's a surprise: a nucleus weighs less than the separate protons and neutrons that make it up. The missing mass is the mass defect. It was released as energy when the nucleus formed, following Einstein's E = mc². That energy is the binding energy. Nuclear masses are measured in atomic mass units (u), and 1 u of mass is equivalent to 931.5 MeV of energy.

Binding energy per nucleon tells you how tightly a nucleus is held. It peaks near iron-56 at about 8.8 MeV. Joining light nuclei, or splitting very heavy ones, moves toward that peak and releases energy.

An unstable nucleus eventually changes into a more stable one by giving off radiation. The three main kinds are:

• Alpha (α) decay: the nucleus throws out a helium-4 nucleus, 2 protons and 2 neutrons. Z drops by 2 and A drops by 4. Uranium-238 becomes thorium-234 this way.
• Beta (β⁻) decay: a neutron turns into a proton, giving off an electron and an antineutrino. Z goes up by 1 and A stays the same. Carbon-14 becomes nitrogen-14 this way. In β⁺ decay, a proton becomes a neutron and gives off a positron.
• Gamma (γ) decay: a nucleus with extra energy releases a high-energy photon. Z and A don't change.

In every decay, the totals of Z and A on each side of the equation match. Alpha particles are heavy and slow and are stopped by paper or skin, but they're dangerous if swallowed or breathed in. Beta particles get through more, and gamma rays need thick lead or concrete to block.

You can't predict when one particular nucleus will decay, but a large sample follows a strict rule: in each half-life, half of whatever is left decays. After n half-lives, the amount left is

N = N₀ × (½)^t/t½

Half-lives range enormously. Iodine-131, used in medicine, has a half-life of about 8 days. Carbon-14's is about 5 730 years, which is why it's used to date things that were once alive. Uranium-238's is about 4.5 billion years, close to the age of Earth.

In fission, a heavy nucleus such as uranium-235 absorbs a neutron and splits into two medium-sized nuclei plus two or three neutrons, releasing about 200 MeV. Those neutrons can split more nuclei, setting off a chain reaction. In a nuclear power plant, control rods soak up spare neutrons so the reaction runs at a steady rate.

In fusion, light nuclei join to make a heavier one. Fusing deuterium and tritium, two isotopes of hydrogen, gives helium-4, a neutron and 17.6 MeV. Fusion powers the Sun, which turns about 4 million tonnes of mass into energy every second. On Earth it's hard to do, because the nuclei must be heated to about 100 million °C before they move fast enough to get past their electric repulsion.

Protons and neutrons aren't the smallest pieces. Each is made of three quarks. A proton is two up quarks and a down quark (uud); a neutron is one up and two downs (udd). Up quarks carry a charge of +⅔ and down quarks −⅓, so the proton's charge adds to +1 and the neutron's to 0.

The Standard Model lists all the known building blocks. There are six quarks and six leptons: the electron, the muon, the tau and three kinds of neutrino. Forces are carried by bosons: the photon carries the electromagnetic force, gluons the strong force, and the W and Z bosons the weak force behind beta decay. The Higgs boson goes with the field that gives many particles their mass. Gravity isn't part of the Standard Model.

To see what's inside particles, physicists smash them together at high speed in particle accelerators. Electric fields speed up charged particles and magnets steer them. The Large Hadron Collider at CERN, near Geneva, is a ring 27 km around that collides protons at energies up to 13.6 TeV. By E = mc², the energy of a collision can turn into new, heavy particles, which is how the Higgs boson was found in 2012.

Nuclear physics began with an accident in a drawer of photographic plates. Within fifty years it had produced the first reactor, and within a century, a complete list of the particles that make up ordinary matter.