Light that comes in stripes, not a smear
Take a glass tube of hydrogen gas, run electricity through it so it glows pinkish-purple, and pass that light through a prism. A glowing lamp filament or the Sun would spread into a continuous rainbow, every colour blending into the next. Hydrogen does something startling instead: the prism throws out just a few thin, brilliant lines of pure colour — one red, one blue-green, two violet — with darkness in between. No smear, no rainbow. Just stripes. This collection of specific colours an element emits is called its atomic spectrum, and the very fact that it comes in separate stripes is the headline of this whole guide.
A puzzle that begged for an explanation
For decades these stripes were a marvellous mystery. Astronomers used them practically — split the light of a distant star, recognise the lines of hydrogen and helium, and you have measured the chemistry of something you can never touch. Helium was actually discovered in the Sun's spectrum before anyone found it on Earth. But *why* the lines fell exactly where they did, nobody could say. A Swiss schoolteacher named Johann Balmer simply stared at hydrogen's four visible lines until he found a numerical pattern that fit them. He had no idea why his pattern worked. It just did.
Soon after, Johannes Rydberg generalised Balmer's pattern into one tidy expression that predicted *every* hydrogen line, visible or not, from a single constant of nature. This is the Rydberg formula, and for years it was an embarrassment of riches: a formula that worked perfectly with no theory behind it. It was a working answer in search of a reason. The reason, when it came, was Bohr's staircase.
The jump that makes the colour
Here is the whole idea in one sentence: a spectral line is an electron jumping between two energy levels. Recall the Bohr model from the last guide, with its staircase of allowed energy levels labelled n = 1, 2, 3 and up. Give an atom a jolt of heat or electricity and its electron leaps up to a higher step. It does not stay there — high steps are uncomfortable — so it drops back down. And when it drops, it has to get rid of the energy difference between the two steps. It releases that exact amount as a single particle of light.
And here is the punchline that ties everything together: the colour of light *is* its energy. A big drop releases a high-energy particle of light, which our eyes read as violet or blue; a small drop releases a low-energy one, which reads as red. Because the steps sit at fixed heights, only certain drops are possible, so only certain energies — only certain colours — can ever come out. That is exactly why the spectrum is stripes and not a smear. Each bright line is one particular fall down the staircase, and its colour is the size of that fall written in light.
Emission, absorption, and dark lines
The staircase runs in both directions, which gives us a clean pair of opposites — together called absorption and emission. When an electron falls *down* a step, it throws out light: that is emission, the bright lines of a glowing gas. When light passes *through* a cool gas, an electron can swallow a particle whose energy exactly matches a step and climb *up*: that is absorption. Absorption removes precisely those colours from the passing light, leaving dark lines in an otherwise full rainbow — at exactly the same positions where the same gas, if hot, would glow.
When the gaps run out: ionization
Recall from the last guide that the steps crowd closer as you climb, funnelling toward a ceiling. The spectral lines do the same: as the jumps reach toward higher and higher levels, the lines bunch together and pile up at a sharp edge called the series limit. Push past that edge and the electron is no longer bound at all — it has escaped the atom completely. The energy needed to lift the electron from its comfortable ground floor all the way out the door is the ionization energy. Remarkably, you can read this escape energy straight off the spectrum, just by finding where the lines stop crowding and the edge falls. The atom's fingerprint even tells you how tightly it grips its own electron.