Although the most catastrophic, the atomic spiral wasn’t the only mystery of the Rutherford atom. Unlike the continuous spectra emitted by heated solids, you’ll recall that excited gases emit and absorb light in the form of distinct spectral lines. The spacing of these is unique to the particular type of gas being observed. In the latter half of the nineteenth century, physicists had become quite good at measuring these line spectra with high precision. Unfortunately, they were much less successful at explaining why the lines were there in the first place.
What’s more, physicists had found that the hot gases would emit radiation at every frequency for which there was an absorption line. However, they found that when light was shone through a cold gas, there was not necessarily an absorption line for every known emission line. Why not? Nobody knew.
In this schematic representation of the frequencies emitted by an excited gas of hydrogen atoms, you can see the spacing between the individual spectral lines decreases steadily at higher and higher frequencies. Note that 1 THz = 1,000,000,000,000 Hz.
More intriguingly, a Swiss schoolteacher by the name of Johann Balmer had discovered a remarkable pattern in the spacing of the spectral lines from hydrogen—the simplest atom, composed of one electron and one proton. He found that the wavelengths of the four lines known at the time were near perfect fractions of the value 3.6456 × 10-7 meters, and those “magic” fractions were 9⁄5, 16⁄12, 25⁄21, and 36⁄32.
As a trained mathematician, it didn’t take him long to realize that the numerators, or top numbers, of these fractions were all squares of numbers: 32, 42, 52, and 62. He also noticed that the denominators, or bottom numbers, were all equal to the numerator minus 22: 32 – 22, 42 – 22, 52 – 22, and 62 – 22. The agreement between these fractions and experimental observation was better than one part per thousand. This was much too close to be a mere coincidence. Moreover, when the next few spectral lines of hydrogen were subsequently discovered, they fit the exact same sequence! Clearly there must be some significance behind this spectral numerology. But what, exactly? Nobody could say.
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