Particle & Nuclear Physics: What Stuff Is Made Of, and What Can Happen to It

A banana is slightly radioactive. It holds potassium, and about one atom in 8,500 of that potassium is the isotope potassium-40, which decays on its own, now and then, with a half-life of about 1.25 billion years. Every day, somewhere in your body, a few thousand of those atoms do it. Nothing pushed them. Nothing about the atom changed. One of its neutrons simply turned into a proton, an electron and an almost undetectable neutrino, and flew apart.

Now ask a stranger question. Why does your banana not do other things? Why does a proton in it sit still for longer than any experiment has been able to measure, when the proton is heavy and could, as far as raw energy goes, fall apart into lighter pieces? A graduate in particle and nuclear physics sees the banana, the proton and the sun as one subject: a short list of ingredients, and a short list of bookkeeping rules about what can turn into what.

Energy is mass, so collisions can make new things

Einstein's best-known equation is usually read as a statement about bombs. Particle physicists read it as a price list. Mass and energy are the same currency, and the exchange rate is the speed of light squared. If you hit two things together hard enough, some of their motion can be spent on a brand-new particle, which then exists until it decays.

The catch is that not all your energy is spendable. Momentum must still balance after the collision, so a particle fired at a stationary target keeps most of its energy as leftover motion. Fire two protons at each other head-on and the whole lot is spendable, because the total momentum is zero. The usable energy is the centre-of-mass energy, written √s. For two beams of energy E head-on it is just 2E. For one beam of energy E on a stationary proton it is only √(2m² + 2mE), in units where c = 1.

A worked number. To make a proton–antiproton pair in a proton–proton collision you need √s of at least four proton masses, 3.75 GeV. With a stationary target that takes a beam kinetic energy of 5.63 GeV, which is why the Bevatron in Berkeley, built to about 6 GeV, found the antiproton in 1955. At a collider you need only about 1.9 GeV in each beam. Try heavier targets below. Producing a Higgs boson of mass about 125 GeV needs roughly 63.5 GeV per beam in a collider, but about 8,600 GeV (8.6 TeV) in a fixed-target beam. That gap is why the biggest accelerators are colliders.

For scale, the Large Hadron Collider has run at 13.6 TeV collision energy since July 2022. Reaching that with a stationary target would need a beam of roughly 98,600 TeV. No ring could hold it.

Quarks and leptons: the short list of what stuff is made of

The Standard Model's list is shorter than the periodic table. Matter particles come in two families. Quarks (up, down, charm, strange, top, bottom) feel the strong force and are never seen alone. Leptons (the electron, muon and tau, each with its own neutrino) do not feel the strong force. Each family comes in three "generations" with the same charges and growing mass; ordinary matter uses only the first: up and down quarks, the electron and its neutrino. Every particle has an antiparticle with opposite charges.

Quark charges are odd: up-type quarks carry +2/3 and down-type −1/3 of a proton's charge. But you never see a third of a charge, because quarks are confined. They only appear glued into bundles with total strong "colour charge" zero: three quarks (baryons), three antiquarks, or a quark with an antiquark (mesons). A proton is two up and one down: 2/3 + 2/3 − 1/3 = +1. A neutron is up, down, down: 0. Build some yourself.

The quarks' bound pairs and triples are by far the biggest source of everyday mass. The up and down quarks together are only about 1% of a proton's mass; the rest is the energy of the strong force binding them, via E = mc². Most of you is binding energy.

Conservation laws decide what can happen

A reaction is allowed if three things hold. Add up the electric charge before and after: it must match. Add up baryon number (quarks count +1/3, antiquarks −1/3) and lepton number, counting each lepton family separately: they must match. And the total energy in the rest masses must be at least that of the products. If a rule is not forbidden by one of these, it happens, at some rate. If it is forbidden, it has never been seen.

Those rules are why the proton, the lightest baryon, is stable. It has nothing lighter with the same baryon number to decay into. Experiments such as Super-Kamiokande in Japan have searched for it to fall apart and found nothing, setting a lifetime limit above 10³⁴ years, many orders of magnitude longer than the universe has existed. In the same spirit, the muon should be able to decay into an electron and a photon on energy grounds alone, but flavour-specific lepton number forbids it, and searches find none at the level of about 1 in a trillion.

Predict first, then check. Pick a reaction, say whether you think it happens, and the page runs the arithmetic.

Heavy messengers have short reach

In quantum field theory, forces are carried by particles. Two electrons repel by swapping photons. The strong force binds quarks by swapping gluons. The weak force, behind the neutron's decay, is carried by the W and Z bosons. And here is the part a graduate remembers: the heavier the carrier, the shorter the force's reach. Borrowing a heavy particle from the vacuum is expensive in energy, so the loan must be repaid quickly, and it cannot travel far. The range is about ħc divided by the carrier's rest energy.

The photon is massless, so electric forces reach across the galaxy. The pion, the lightest meson at 139.6 MeV, gives 1.41 fm, which is why the nuclear force binds neighbours in a nucleus and fades beyond. The W boson (80.4 GeV) gives 0.0025 fm, about 300 times smaller than a proton. That is why the weak force is "weak" at ordinary distances: it hardly reaches.

Binding energy: why the sun shines and reactors run

A nucleus weighs a little less than its separate protons and neutrons. The missing mass, multiplied by c², is the binding energy, the work needed to pull it apart. Divide by the number of nucleons A and you get a curve with a shape every nuclear scientist knows: it rises steeply for light nuclei, peaks around iron and nickel (about 8.8 MeV per nucleon), then falls slowly to uranium.

Anything that moves a nucleus up the curve releases energy. Light nuclei going up by fusing; heavy ones going up by splitting. Worked numbers from measured masses: helium-4 has 7.07 MeV per nucleon, iron-56 8.79, uranium-235 7.59. Deuterium plus tritium fusing into helium-4 and a neutron frees 17.6 MeV, about 3.4 × 10¹⁴ joules per kilogram of fuel. Fission of uranium-235 frees roughly 200 MeV per atom, about 8 × 10¹³ J/kg. TNT is 4.2 × 10⁶ J/kg: fusion fuel carries about 80 million times as much.

The same curve explains the sun, which fuses hydrogen into helium, and why stars much heavier than the sun make iron and stop: past iron, fusion costs energy instead of paying it. That is the hinge to Astrophysics & Cosmology (34/88).

Decay is random, yet the curve is exact

An unstable nucleus has no clock. A carbon-14 atom that has survived 5,730 years is exactly as likely to decay in the next minute as one made a second ago. So nothing in any single atom tells you when it will go. Yet a sample of trillions behaves with high precision: after one half-life, half remain; after two, a quarter.

Carbon dating uses it: living things hold carbon-14 at the atmosphere's level and stop taking more when they die. A bone with a quarter of the level has lived two half-lives, about 11,460 years. After 20,000 years only about 8.9% remain, which is why the method runs out near 50,000 years. The half-lives span an enormous range: below, from microseconds to billions of years. Watch the randomness shrink as the sample grows.

With 10 atoms, the survivors after one half-life can easily be 3 or 7. With 1,000, they are close to 500 every time. That is the whole content of "the law of large numbers", and the reason a particle detector needs many events before it says anything.

Where the Standard Model runs out

The Standard Model is the most precisely tested theory in science, and every physicist expects it to be incomplete. The decisive experiments: neutrinos oscillating between flavours, which means they have mass (Super-Kamiokande and SNO, Nobel Prize 2015); the Higgs boson, announced on 4 July 2012 by ATLAS and CMS at about 125 GeV; and the muon's magnetic moment, where Fermilab's final 2025 result is 127 parts per billion precise and where theory predictions were revised, shrinking a famous disagreement.

What is left? Neutrinos have mass but tiny: the KATRIN experiment's 2025 limit is under 0.45 eV, at 90% confidence, at least a million times lighter than the electron, and the Standard Model does not say why. Dark matter makes up about five times as much as ordinary matter, and no Standard Model particle fits. The universe has far more matter than antimatter, and the model's known effects are too small to explain it. Gravity is not in the model at all. These are open, and physicists disagree on which gap will give first.

What a graduate just sees

• Mass is a form of energy, and a collision can turn motion into new particles, if the centre-of-mass energy is enough.
• Colliders beat fixed targets because head-on collisions waste no energy on leftover motion.
• Quarks only come in colourless bundles. A proton's mass is mostly binding energy, not quark mass.
• Before asking if a reaction happens, check charge, baryon number, lepton number and energy.
• The heavier the force carrier, the shorter the force's range: ħc over mass.
• Energy per nucleon peaks at iron: fusion pays below it, fission pays above it.
• Each atom's decay is random with no memory; a crowd's decay is exponential and exact.
• A very large number of events is the only way to see rare processes.

Where it shows up next

• Astrophysics & Cosmology (34/88): the binding-energy curve decides which stars make which elements, and the first minutes of the universe were particles interacting at colliders' energies and above.
• Condensed Matter Physics (34/87): the same quantum field ideas return as "quasi-particles" inside solids.
• Medicine: PET scanners detect the photons from positron annihilation, proton therapy aims beams at tumours, and technetium-99m (half-life 6 hours) is the commonest imaging isotope.
• Energy: fission reactors, fusion projects such as ITER, and radiocarbon dating all lean on the same curve and the same decay law.
• Computing: the web was invented at CERN, and detectors produce so much data that the trigger systems discard most events in microseconds.

If you want to go deeper

• 📘 Textbook. David Griffiths, Introduction to Elementary Particles (Wiley-VCH, 2nd revised edition, 2008). Clear and short; the usual first particle-physics book after quantum mechanics.
• 📘 Textbook. Mark Thomson, Modern Particle Physics (Cambridge, 2013). More modern and more demanding, and the course text at Cambridge.
• 📘 Nuclear. Kenneth Krane, Introductory Nuclear Physics (Wiley, 1988). The standard undergraduate nuclear text.
• 📘 Gentler. Frank Close, Particle Physics: A Very Short Introduction (Oxford, 2004). No equations, one afternoon.
• 🌐 Free course. MIT OpenCourseWare 8.701 Introduction to Nuclear and Particle Physics (Fall 2020): notes, videos, problem sets and solutions.
• 🌐 Reference. The Particle Data Group's Review of Particle Physics: every measured mass and lifetime, free.