The Fundamental Constant
Bohr’s model, which simplistically modeled electrons as charged, spin-less particles orbiting the nucleus at speeds much lower than the speed of light, successfully explained the coarse structure of atoms, but not the additional fine structure.
That required another advance which came in 1916 when Physicist Arnold Sommerfeld had a realization.
If you modeled Hydrogen atom as Bohr did, but took the ratio of ground-state electron’s velocity and compared it to the speed of light, you would get a very specific value which Sommerfeld called α – The Fine Structure Constant.
This constant, once folded into Bohr’s equations properly, was able to precisely account for energy difference between coarse and fine structure predictions.
In terms of the other constant known at the time, α = e2/4πε0ħc, where; e is electron’s charge, ε0 is the permittivity constant, ħ is Planck’s constant and c is speed of light.
Unlike these other constants which have units associated with them, α is truly dimensionless constant, which means it is simply a pure number with no units associated with it at all.
While the Speed of Light may be different if you measure it in meters/second, feet/year, miles/hour, or any other unit, α always has the same value.
For this reason, it is considered to be one of the fundamental constants that describe our Universe.