The Rydberg equation is probably the best method.
= 10973731.568160(21), m-1
“m sub e” is the rest mass .
The Electron
,
“e” refers to the elementary charge
,
“epsilon naught” refers to permistivity of free space .
,
“h” is Planck constant
And
“c” stands for the speed at which light is traveling.
in vacuum.
This constant is one of the most exact in the world. It has an uncertainty of less that 2 out of every trillion. Therefore, it provides a very precise verification for the electron’s rest mass.
There are many other methods. The first was to calculate the charge/mass ratio, then divide the charge by this ratio. This was possible following the Millikan oil drop experiment, where he determined electron charge (JJ Thompson previously determined this ratio).