Why does the small world come in steps?

In 1814 the German lens maker Joseph von Fraunhofer looked at sunlight through a very good prism. He expected a smooth rainbow. Instead he found hundreds of thin dark lines across it, as if someone had cut gaps in the colours. He mapped more than 500 of them.

Nobody could explain the gaps. But they never moved. The same lines sat at the same colours every time.

In 1859 and 1860 Gustav Kirchhoff and Robert Bunsen (of the Bunsen burner) heated different elements in a flame and split the light. Each element gave its own set of sharp coloured lines, and never any others. Sodium always gave a bright yellow pair. Hydrogen, glowing in a gas tube, always gave the same four lines you just saw.

They then noticed something striking. The dark lines in sunlight sat at exactly the same colours as the bright lines from elements on Earth. A cool gas soaks up the very colours it gives out when hot. So the dark lines were fingerprints: the Sun's outer layers contained hydrogen, sodium, iron and more.

In 1868 astronomers found a line in sunlight that matched no element on Earth. The English astronomer Norman Lockyer named the new element after the Greek word for the Sun: helium. Chemists only found helium on Earth in 1895.

One more puzzle broke the old physics. Heat a lump of metal and it glows dull red, then orange, then white. The physics of 1900 predicted that any hot object should pour out unlimited ultraviolet light. That obviously doesn't happen, or every fire would blind you.

In 1900 Max Planck found a fix. He assumed that a glowing object can only give out energy in small fixed packets, not in any amount it likes. The size of each packet depends on the colour: blue packets carry more energy than red ones. With that one assumption, his formula matched the measurements exactly.

Planck called each packet a quantum, from the Latin for "how much". That's where the word comes from. Quantum physics began as the discovery that energy comes in steps.

In 1913 the Danish physicist Niels Bohr put the pieces together. He proposed that an electron in an atom can only have certain fixed energies. Picture a ladder. The electron can stand on any rung, but never between rungs. Physicists call each rung an energy level.

The bottom rung is where the electron normally sits. Heat, electricity or light can push it up to a higher rung. It doesn't stay there long. Soon it drops back down, and when it does it gives out the difference in energy as one photon, one particle of light.

Because the rungs are fixed, the drops are fixed. Because the drops are fixed, so are the colours.

A bigger drop releases more energy, and a photon's energy sets its colour. Red light carries the least energy of the colours you can see, and violet the most. So a short drop gives red, and a long drop gives violet. A drop all the way to the bottom rung carries so much energy that the light is ultraviolet, which your eyes can't see.

This is Fraunhofer's mystery, solved. An atom can only soak up a photon whose energy exactly matches one of its gaps. Every other colour passes straight through. So a cool gas in front of a hot light removes its own colours, leaving dark lines exactly where the bright lines would be.

Bohr's ladder worked brilliantly, but he couldn't say why the rungs existed. The answer came in 1924 and 1925 from Louis de Broglie, Werner Heisenberg and Erwin Schrödinger.

The key idea: an electron in an atom behaves like a wave, spread around the centre of the atom. Think of a guitar string. Pinned at both ends, it can only vibrate in certain patterns: one hump, two humps, three humps. Nothing in between fits. Each pattern gives a different note.

An electron wave held by an atom works the same way. Only certain wave patterns fit, and each pattern has its own energy. Those patterns are the rungs. The steps aren't random. They're what happens whenever a wave is held in a small space.

The old physics had a nasty prediction. A circling electron should give off light all the time, lose energy and spiral into the centre of the atom in a fraction of a second. Every atom in the universe would collapse.

The wave picture fixes this. The bottom rung is the lowest pattern that fits. There's no lower rung to fall to, so the electron stays put. Atoms are stable because of quantum rules, not in spite of them. Optional page 1b goes deeper.

Once you know about energy steps, you'll see them everywhere.

LEDs. In an LED, electrons drop across a fixed energy gap in a specially made crystal. Engineers pick the material to set the size of the gap, and so the colour. The blue LED needed a new material, and won the 2014 Nobel Prize in Physics for Isamu Akasaki, Hiroshi Amano and Shuji Nakamura. Blue made white LED lighting possible.

Lasers. A laser gets huge numbers of atoms to drop the same rung at the same moment, in step. Every photon comes out the same colour and in the same direction. Albert Einstein worked out the rule behind this in 1917, and the first laser shone in 1960. Optional page 1a explains how.

Atomic clocks. Caesium atoms flip between two energy levels at an exact rate. Since 1967 the world has defined the official second as 9,192,631,770 of those flips. The best optical clocks use atoms such as strontium and are so precise that, in theory, they wouldn't gain or lose a second in about 15 billion years, longer than the age of the universe.

The northern lights. Particles from the Sun knock electrons in the upper air up a rung. Oxygen atoms drop back and glow green, at 557.7 nm. Nitrogen adds blues and purples.

Astronomy. Every star's colours carry its fingerprint. That's how we know what the universe is made of.