Hydrogen

Exact Steps

An electron in an atom can take only certain patterns, each with its own exact energy. Hydrogen is the one neutral atom whose energies follow a rule short enough to write in a line. Freeing its electron from the lowest pattern takes 13.6 electronvolts, the energy an electron gains crossing 13.6 volts; a photon of visible light carries about two or three. The next pattern up is held by a quarter of that, the third by a ninth, the fourth by a sixteenth: each by 13.6 divided by the square of its number.

So the steps crowd closer and closer together toward the top, where the electron goes free. The patterns grow as they rise, also as the square of their number. The second is four times as wide as the first, and the hundredth ten thousand times, as wide as a bacterium.

Each sharp color hydrogen gives out marks one fall from a higher step to a lower one: the electron’s cloud changes to the lower step’s pattern, and the light carries away the difference. Falls that end on the second step give its visible colors. The four brightest are red from the third step, blue-green from the fourth, blue from the fifth and violet from the sixth, and falls from higher steps add fainter violet lines, crowding together into the ultraviolet. The red is the glow of the gas cloud above, where the ultraviolet light of young stars frees electrons, and each one caught again falls back down the steps. Falls to the lowest step are bigger and give ultraviolet; falls to the third give infrared.

The rule was found in the colors first, and explained only later. Quantum physics gets it exactly from two things: the pull of the proton on the electron, and the electron as a wave, held in place by that pull, which can ring only in certain patterns.

Measured to a Trillionth

Because hydrogen is so simple, its colors can be worked out by theory and measured in the laboratory more precisely than almost anything else in nature. That makes it the place where the theory of light and matter, quantum electrodynamics, is tested hardest inside an atom. Lasers held steady by atomic clocks now pin several of its lines down to better than a part in a trillion. One ultraviolet line, between the lowest step and the second, is known to almost fifteen digits. In 2026 the violet line, from the sixth step to the second, was measured to seven parts in ten million million. Given that ultraviolet line and the proton’s size, measured another way, the theory predicted the same number at least as closely.

At that precision the steps are not quite 13.6 divided by the square of their number. They are nudged by relativity, by the electron acting on itself through its own field, and by the size of the proton, whose charge is spread over a tiny ball rather than packed into a point. So hydrogen’s light measures the proton. For a decade that measurement gave a proton four percent larger than hydrogen made with a muon, the electron’s heavier cousin, in its place. The newest measurements of ordinary hydrogen, the 2026 one among them, agree with the muon: about 0.84 femtometers. A few older ones still sit a little higher.

Even hydrogen’s antimatter twin has been made and measured: antihydrogen, a positron bound to an antiproton, held in a magnetic trap. Its ultraviolet line matches hydrogen’s to two parts in a trillion.

A Radio Whisper

Even the lowest step is split in two. The proton and the electron each carry spin, and each is a tiny magnet. The atom holds a hair less energy when their spins point opposite ways. An atom whose electron’s spin flips from pointing the same way as its proton’s to the opposite way gives out a radio wave 21 centimeters long. Left alone, an atom waits on average about 11 million years to flip. In a gas, collisions turn spins both ways far more often, with no radio wave, and keep about three atoms in four in the higher state, ready to flip.

Yet there is so much hydrogen between the stars that whole galaxies glow at that wavelength, and radio waves pass straight through the dust that hides most of the Milky Way from our eyes. Radio telescopes map the hydrogen by it: the spiral arms of our own galaxy, and the gas circling in the outskirts of others. That gas circles faster than all the stars and gas we can see could hold it, one of the first signs of dark matter.

Radio telescopes have now measured the hydrogen in tens of thousands of galaxies, and the expansion of space, stretching each galaxy’s wave, tells how far off each one is. Others listen for the whisper of the hydrogen that filled universe as the first stars lit up, stretched to several meters long. One experiment reported it in 2018; a later one with a different design found nothing at that level, and the question is not settled. The same flip, made to repeat in a hydrogen maser, keeps steady time aboard navigation satellites and beside radio telescopes.

Two Atoms, One Cloud

Pressed together, atoms with full outer clouds push each other away. Two hydrogen atoms do the opposite: their clouds run together into one. Each brings one electron, and two electrons may share a pattern if their spins point opposite ways. The shared cloud gathers between the two protons and pulls on both, holding them 0.074 nanometers apart. That is the hydrogen molecule, the simplest bond between two atoms, and pulling it apart takes 4.5 electronvolts. Joining gives those 4.5 electronvolts out, and something has to carry them off, a third atom or, in space, a grain of dust; two lone atoms that meet almost always bounce apart again.

Hydrogen gas is the lightest there is. High in the air its atoms are so light and quick that some escape into space: Earth loses about three kilograms of hydrogen every second. Squeezed hard enough, hydrogen turns into a metal. Deep inside Jupiter and Saturn, millions of times the pressure of our air press it into a liquid metal, and the currents in it are thought to make Jupiter’s strong magnetic field. In the laboratory, shock waves have briefly made hot liquid hydrogen conduct like a metal. Cold solid hydrogen squeezed between the tips of two diamonds to more than four million atmospheres shows signs of turning metallic too; whether it fully has is still debated.

Fuel of the Stars

For most of their lives, stars shine by fusing hydrogen into helium. The Sun turns about 600 million tonnes of hydrogen into helium every second. The helium weighs a little less, because fusing gives off energy, and anything that gives off energy loses mass. The energy leaves, nearly all of it as the light the Sun sends out, and that alone makes the Sun about four million tonnes lighter every second. The fusing itself is slow. To start, one proton must turn into a neutron in the brief moment that two meet, and only the weak force can do that, so a proton in the Sun’s core waits billions of years for it. In 4.6 billion years the Sun has used about half the hydrogen at the very center of its core.

i Hydrogen fuses only in the core, the white-hot middle ×

On Earth, fusion experiments burn heavy hydrogen instead, which fuses far more readily. Deuterium has a neutron in its nucleus, and about one hydrogen atom in 6,400 in seawater is deuterium. Tritium, which is radioactive, has two. At the end of 2022 a laser facility first got more energy out of a fuel pellet than its lasers delivered. By 2025 it got four times as much out as the lasers delivered. The lasers still draw far more power from the grid than the pellets give back, and no power plant yet runs on fusion.