In the Bohr model of the atom, an electron may only occupy certain allowed orbits, its energy levels, and nothing in between. While it stays on one level it gives out no light. Light comes out only when the electron jumps down from a higher level to a lower one, and the light carries away exactly the difference in energy. In hydrogen, the jump from level 3 to level 2 always gives the same red light, at a wavelength of 656 nanometres. Niels Bohr, born in Copenhagen on 7 October 1885, published the idea in July 1913.
An atom that should not exist
By 1912 physicists had a picture of the atom with a small, heavy nucleus and electrons circling it. The trouble was what classical physics said about that picture. In 1897 Joseph Larmor had shown that an accelerating electric charge radiates energy, and an electron going round in a circle is always accelerating. So it should keep shining, keep losing energy and spiral in. Atoms built on the classical rules would be unstable. Yet the atoms around us sit there quite happily.
Steps, not a ramp
Bohr’s answer, in the Philosophical Magazine in July 1913, was not to repair classical physics but to set part of it aside. He proposed that the electron may only move in certain orbits, which he called stationary states. In those orbits, and only there, it does not radiate. There are no orbits in between.
Think of a staircase instead of a ramp. You can stand on any step, but not halfway between two of them. To change height you have to jump, and a jump has a definite size.
For hydrogen the steps have definite energies, roughly −13.6 electron volts divided by the square of the step number n:
One jump, one colour
When the electron drops from a higher step to a lower one, the energy it loses leaves as light. Bohr tied the two together with Planck’s relation, E = hf: the bigger the drop, the higher the frequency of the light. Because the steps are fixed, so are the drops, and so is the colour each drop produces.
The drop from step 3 to step 2 gives red light at 656 nanometres, the first line of what is called the Balmer series. It is the same red every time, in every hydrogen atom.
That is why glowing hydrogen does not give a smooth rainbow. Pass its light through a prism and you see a few sharp, separate lines on a dark background, one for each possible jump. Bohr’s model reproduced the formula that described those lines, the Rydberg formula, and even gave the value of its constant from more basic quantities.
What survived
The Bohr model did not last in its original form. In the 1920s it was replaced by quantum mechanics, which no longer pictures the electron moving along a neat circular path. But the central idea survived the replacement: an atom’s electron can only have certain energies, and the light an atom gives out is a record of the jumps between them. The Short draws it as a staircase with a red flash between two steps.
Every sharp line in a spectrum is one step down a staircase. And that’s how we found out.
