Sommerfeld, discoverer of the Fine Structure Constant
Practically every physical constant consists of a number multiplied by one or more physical units. e.g.
c = 3e8 m/sec. (1)
The number part changes with a different choice of units. e.g.
c = 3e10 cm/sec. (2)
Of all the physical constants, one stands out in that it is dimensionless. That constant is called The Fine Structure Constant. It is symbolized by “α” and equals approximately 1/137. More precisely
α = e2/2eohc. (3)
Since it is dimensionless, α is the same in every system of units.
Many physical quantities can be expressed as α times the physical units of choice. For example, the speed of a Bohr atom ground state electron can most simply be expressed as
v = αc. (4)
Or more generally
vN = αc/N. (5)
A second useful constant is
α’ = h/(2πmcα), (6)
where m is the electron’s mass. α’ has the dimension “meter”, and the radius of the Nth electron orbital isrN = N2α’. (7)