Concepts explained
Why the Electron Does Not Fall — A Jump With No Middle
By the theory of the day, an atom should collapse in a hundred-billionth of a second. Yet here we are. The single assumption a twenty-eight-year-old Bohr made to escape that contradiction went on to explain firework colours, the composition of stars, and where an electron may sit.
Following that question leads inside the atom — and there physics ran aground once more.
Not a rainbow but a few stripes
Send a sodium flame through a prism. You might expect a rainbow. Instead, against darkness, a few yellow stripes.
Hydrogen gives its own stripes, helium its own — different in place and number for every element. These are .
But something is odd here. Why only a few stripes?
The colour of light is the size of an lump (article one). Emitting only a few colours means emitting only a few sizes. Not any size at all.
The atom cannot exist
By 1911 the inside of the looked like this: a tiny, heavy at the centre with electrons going round it. A solar system in miniature.
A plausible picture — until you calculate. Electromagnetism, well established by then, says that a charge moving in a circle radiates light. Radiating, it loses energy; losing energy, its orbit spirals inward.
Worse, as the orbit shrank continuously the emitted colour would shift continuously too. A rainbow should come out. A few stripes come out instead. Two things fail at once.
Bohr's prescription
In 1913 Niels Bohr got past the problem exactly as Planck had in the first article: not by explaining, but by assuming.
- The places an electron may occupy are fixed. Not just anywhere.
- While it sits in one of them it emits nothing. Do not ask why.
- Only in moving between them does it emit the difference in energy as light.
Spectral lines drop straight out of the third assumption. Fixed seats mean fixed gaps between seats, and fixed gaps mean a fixed handful of colours. Different elements have different seating, so different combinations.
And the first assumption explains why the atom holds together.
Bohr also computed where hydrogen's seats lie. The colours implied by the gaps matched hydrogen's already-measured spectral lines.
There is no middle
Moving between seats is called a — and here is the truly strange part.
The everyday usage is the exact opposite, which is worth noticing. A business making a leap is said to make a quantum jump, whereas a real one is among the smallest changes nature performs. The point was never the size. The point is that there is no middle.
A little further in
Bohr's assumptions gave the right numbers and explained nothing. Why those seats? Why no radiation while seated? No answer.
What set him off was a single formula.
A schoolteacher's arithmetic
In 1885 Johann Balmer of Switzerland was a schoolteacher past sixty. Studying the wavelengths of four hydrogen lines, he found that a single simple ratio formula produced all of them.
He had no idea why. The numbers simply came out. Physicists treated it as numerology and passed over it for nearly thirty years.
Bohr saw the formula early in 1913 and, by his own account, had the skeleton of his paper within days.
As soon as I saw Balmer's formula, the whole thing was at once clear to me.Bohr, recalling 1913
But why those seats
In 1924 Louis de Broglie offered a short argument in his doctoral thesis.
had long been a , and in the first article it turned out to be a grain as well. Then, for symmetry, should the electron not be a wave as well as a grain? That was the whole argument.
And Bohr's seats follow from it. If the electron is a , then after one lap of the orbit the wave must meet itself in step. Only orbits whose circumference holds a whole number of wavelengths survive.
His examiners, unsure what to make of the thesis, sent it to Einstein. His verdict:
He has lifted a corner of the great veil.Einstein, on reading de Broglie's thesis
Broken apparatus confirms it
Bell Labs, New York, 1927. Clinton Davisson and Lester Germer were firing electrons at a piece of nickel when their glass apparatus broke and the nickel was exposed to air.
Heating it at length to clear the oxide made the nickel's crystal grains grow large. On repeating the experiment, a pattern appeared that had not been there before: the electrons, passing through the regular lattice, were making .
- 1885Balmer — fits a formula to hydrogen's lines without knowing why
- 1911Rutherford — a nucleus at the centre. But then the atom collapses
- 1913Bohr — assume the seats are fixed, and Balmer's formula follows
- 1924de Broglie — if the electron is a wave, those seats are explained
- 1927Davisson and Germer — broken apparatus confirms matter waves
This picture does not last either
In de Broglie's picture the electron still goes round an orbit — a wave riding the orbit rather than a grain. Most textbook diagrams of the atom stop here.
But being a wave brings an awkward question. A wave is not at a point; it is spread out. So where on the orbit is the electron? Everywhere on it?
Two years later Schrödinger answered — and his answer was that there are no orbits at all.
The question that remainsIf the electron is a spread-out wave, where does the spread go when we catch electrons one at a time? And what was spread out in the first place?