What matter is made of

October 16, 2026

Everything you can touch is made of atoms, and a glass of water holds about 2.5 × 10²⁵ of them, millions of times more than there are grains of sand on all of Earth's beaches. Atoms come in 118 kinds, called elements, and about 90 of them occur in nature. Each atom is a tiny, heavy nucleus of protons and neutrons with a cloud of electrons around it. The protons and neutrons are in turn made of quarks.

How atoms are built explains most of the physical world. It explains why copper conducts electricity and glass doesn't, and why sodium explodes in water while neon reacts with nothing. It also explains why the Sun shines and what a nuclear reactor runs on. All of it follows from a few particles and the forces between them.

The parts of an atom

An atom has three kinds of part. Protons carry a positive charge and neutrons carry none, and together they form the nucleus at the centre. Electrons carry a negative charge exactly as big as the proton's, and they spread out in a cloud around the nucleus. An atom has as many electrons as protons, so the charges cancel and the atom as a whole is neutral.

The number of protons, called the atomic number, decides which element an atom is. Every atom with 6 protons is carbon, every atom with 8 is oxygen, and every atom with 79 is gold. A common carbon atom has 6 protons, 6 neutrons and 6 electrons.

Almost all the mass sits in the nucleus. A proton and a neutron weigh about the same, and each is 1,836 times heavier than an electron, so a carbon atom's nucleus holds 99.97% of its mass. The nucleus is also about 10,000 times smaller across than the atom, so it holds nearly all the mass in less than a trillionth of the volume. The rest of the atom's size is the electron cloud, and the cloud is what touches other atoms, so it decides how atoms bond, conduct and feel.

The electron cloud

An electron in an atom doesn't orbit the nucleus like a planet. It behaves as a wave spread out around the nucleus, and the wave gives the probability of finding the electron at each point. Any single measurement finds the electron at one spot, but many measurements trace out the shape of the wave.

The electron in hydrogen is most likely to be found 0.053 nm from the nucleus, a distance called the Bohr radius. The cloud has no sharp edge, but it thins out quickly, so an atom has a definite working size: hydrogen is about 0.1 nm across, and the largest atoms are about 0.6 nm.

Why electrons don't fall into the nucleus

The electron is negative and the nucleus is positive, so they attract, and the closer they are the more energy the attraction releases. The electron doesn't fall in, because squeezing a wave into a smaller space raises its energy. A wave held between walls has to fit between them, so a narrower space forces a shorter wavelength, and for an electron a shorter wavelength means more energy. The energy of the lowest wave in a box of width L is:

Here h is Planck's constant and m is the electron's mass. Halving the box multiplies the energy by four.

This sets the size of atoms. Holding an electron within 0.1 nm costs about 38 eV, which is the same scale as the 13.6 eV that binds hydrogen's electron. Squeezing it into 0.01 nm would cost a hundred times as much (1/L²), while the electric attraction would only gain ten times as much (1/L). So pulling the electron closer costs more than it gains, and the electron settles at the distance where the two balance, about 0.05 nm.

Orbitals and shells

The electron's wave around the nucleus can only take certain shapes, the 3D standing waves called orbitals. A guitar string can only vibrate at notes that fit its length, and an electron can only have the energies of the orbitals that fit around the nucleus. So an atom's electrons sit at fixed energies, and when an electron drops to a lower one, the atom gives off light carrying exactly the difference. Those sharp colours are why neon signs glow red and sodium streetlights glow orange.

Orbitals are named by a shell number and a shape. The shell number (1, 2, 3, …) sets the size and roughly the energy, and the letter sets the shape. An s orbital is round, a p orbital has two lobes, and a d orbital has four lobes, or two and a ring. Shell 1 has just one s orbital, shell 2 has one s and three p, and shell 3 adds five d.

Each orbital holds at most two electrons, which have opposite spins. This rule is the Pauli exclusion principle, and almost all of chemistry follows from it. Without it every electron would drop into the lowest orbital and all atoms would behave alike. With it, electrons stack up into higher and higher orbitals as atoms get bigger: shell 1 holds 2 electrons, shell 2 holds 8, and the next 8 fill the s and p orbitals of shell 3.

The electrons in the outermost shell are the valence electrons, and they set how an atom behaves, because they are the ones that meet other atoms. A full outer shell is especially stable. Atoms with one or two electrons beyond a full shell give those electrons away easily, and atoms one or two short of a full shell pull electrons in.

The periodic table

The periodic table lays the elements out in the order their shells fill. Each row starts a new shell, and each column holds elements with the same number of outer electrons, so the elements in a column behave alike. Lithium, sodium and potassium in column 1 each have one outer electron, and all three react violently with water. Helium, neon and argon in the last column have full shells and react with almost nothing.

The left and middle of the table are metals. Their atoms hold their few outer electrons loosely, so when metal atoms pack together, those electrons leave their own atoms and roam through the whole solid. That shared sea of free electrons is why metals conduct electricity and heat, why they are shiny, and why they bend instead of shattering. Copper has one free electron per atom, about 8.5 × 10²⁸ of them in every cubic metre, which Electricity follows through a wire.

The top right of the table holds the non-metals, which are close to a full shell and hold their electrons tightly. With no free electrons they don't conduct, which is why glass, plastic and rubber are insulators. Between the two sits a diagonal band of metalloids, among them silicon, which conduct a little and can be tuned to conduct more, the property every computer chip is built on. How atoms share and trade outer electrons to form molecules is the subject of Molecules and chemistry.

Inside the nucleus

The protons in a nucleus all repel each other, and at that distance the repulsion is huge. Two protons 1 fm apart push on each other with about 230 N, the weight of a 23 kg mass, on particles that each weigh 10⁻²⁷ kg. A different force holds them together: the strong force. It attracts protons and neutrons to each other, it is about 100 times stronger than the electric force at close range, and it doesn't care about charge. Its range is very short, though, and it fades to nothing beyond about 3 fm, the width of two or three nucleons.

That short range limits how big a nucleus can be. Each proton or neutron only feels the strong pull of its immediate neighbours, but every proton repels every other proton in the nucleus. Neutrons add strong attraction with no repulsion, so bigger nuclei need extra neutrons to hold together.

Atoms of one element with different numbers of neutrons are isotopes. They have the same electrons, so they behave the same chemically, but their nuclei differ. Carbon-12 has 6 neutrons and makes up 98.9% of all carbon, while carbon-14 has 8 and is unstable. An unstable nucleus eventually changes into a stable one by radioactive decay, in one of these ways:

• Alpha decay: the nucleus throws out a helium nucleus (2 protons and 2 neutrons). Heavy nuclei like uranium decay this way.
• Beta decay: a neutron turns into a proton, an electron and an antineutrino, and the electron flies out. Carbon-14 decays this way into nitrogen-14.
• Gamma decay: a nucleus left with extra energy releases it as a high-energy photon, without changing its protons or neutrons.

No one can predict when a single nucleus will decay, but a large group decays at a fixed rate. The half-life is the time for half of the nuclei to decay, and after n half-lives a fraction (1/2)ⁿ is left:

Carbon-14's half-life is 5,730 years. Living things keep topping up their carbon-14 from the air, and stop when they die, so the fraction left in old wood or bone dates it.

Inside protons and neutrons

Protons and neutrons are each made of three quarks. Two kinds of quark are enough for ordinary matter. The up quark has a charge of +2/3 and the down quark has −1/3, in units of the proton's charge. A proton is two ups and a down, so its charge is 2/3 + 2/3 − 1/3 = +1. A neutron is one up and two downs, so its charge is 2/3 − 1/3 − 1/3 = 0.

The quarks are held together by gluons, the particles that carry the strong force. The strong force between quarks behaves oddly: it doesn't weaken as they move apart, and stays at about 150,000 N, the weight of 15 tonnes, however far they go. Pulling two quarks apart stores more and more energy in the gluon field between them, until there is enough to create a new quark and antiquark from it (E = mc²). The new quarks pair up with the old ones, so you get two particles and never a lone quark. No one has ever seen a single quark on its own, and this is why.

The three quarks' own masses add up to only about 9 MeV/c², roughly 1% of the proton's 938 MeV/c². The other 99% of the proton's mass is the energy of the quarks' motion and of the gluon field binding them, because energy has mass, by E = mc². So most of the mass of everything around you, including your body, is the energy of the strong force inside protons and neutrons.

The Standard Model

The Standard Model is the theory of every particle known. It has 12 matter particles and 5 others, and it has matched almost every particle experiment for 50 years. The matter particles come as 6 quarks and 6 leptons. Leptons are the particles that don't feel the strong force: the electron, its two heavier copies the muon and tau, and three neutrinos, which are almost massless and barely interact with anything.

The matter particles come in three generations, each a heavier copy of the one before. Only the first generation is stable, because heavier particles decay into lighter ones in a fraction of a second, so everything around you is built from up quarks, down quarks and electrons. The heavier ones only show up in cosmic rays and particle colliders.

Every force between particles is carried by a particle of its own. Two charges push on each other by exchanging photons, quarks bind by exchanging gluons, and the W and Z bosons carry the weak force, which turns neutrons into protons in beta decay. The Higgs boson is the ripple in the Higgs field, which gives the W and Z bosons, quarks and charged leptons their mass. It was the last piece found, at CERN in 2012.

Gravity is far too weak to matter between particles: the electric repulsion between two protons is 10³⁶ times their gravitational attraction. It dominates at large scales only because masses always attract, while positive and negative charges cancel out in bulk.

Every particle also has an antiparticle with the same mass and opposite charge. The electron's is the positron, which hospitals use in PET scans. When a particle meets its antiparticle they annihilate into energy. The Big Bang should have made equal amounts of both, and why the universe is made almost entirely of matter is still unexplained.

Modern physics describes each kind of particle as a ripple in a field that fills all of space: there is one electron field, and every electron in the universe is a ripple in it. That is why every electron is exactly identical.

The Standard Model leaves known gaps, and the theories that try to fill them are unproven:

• Gravity isn't part of it, and no tested theory combines gravity with quantum mechanics. String theory, which models particles as tiny vibrating strings, is one attempt, but it hasn't made a prediction that experiments could check.
• Dark matter makes up about 85% of the matter in the universe. Its gravity shows in how galaxies spin, but no experiment has detected a dark matter particle, and none of the Standard Model's particles fit.
• Dark energy is speeding up the expansion of the universe, and nobody knows what it is.
• Neutrino masses aren't zero, which the original model assumed.

Nuclear energy and where elements come from

A nucleus weighs slightly less than the protons and neutrons that make it up, and the missing mass is the energy that was released when they bound together:

The binding energy per nucleon measures how tightly each proton or neutron is held, and it varies across the elements. It rises steeply through the light elements, peaks near iron and nickel, and falls slowly for heavier ones. Any nuclear reaction that moves toward the peak releases energy.

Fusion joins light nuclei into heavier ones. The Sun fuses about 600 million tonnes of hydrogen into helium every second, and 0.7% of that mass, about 4 million tonnes per second, leaves as sunlight. Fission splits heavy nuclei instead, and a uranium-235 nucleus releases about 200 MeV when it splits. A kilogram of uranium-235 releases about 8 × 10¹³ J, while burning a kilogram of coal releases about 24 MJ, so uranium holds about 3 million times as much energy per kilogram. Chemistry only rearranges electrons, held by the electric force at atomic distances. Nuclear reactions rearrange protons and neutrons, held by the far stronger strong force at distances 10,000 times smaller.

The binding-energy curve also explains where the elements came from:

1. The Big Bang made hydrogen, helium and a trace of lithium.
2. Stars fuse those into heavier elements up to iron. Past iron, fusion absorbs energy instead of releasing it, so a star's core can't burn further.
3. Supernovae and collisions of neutron stars make the elements heavier than iron in bursts of neutron capture. Much of the gold and platinum on Earth was made in neutron star collisions.

So nearly every atom in your body other than hydrogen was made inside a star that exploded before the Sun formed.