If the electron is moving at a relativistic velocity, any measurement must use the correct expression for mass.
Since the electron mass determines a number of observed effects in atomic physics, there are potentially many ways to determine its mass from an experiment, if the values of other physical constants are already considered known.
Historically, the mass of the electron was determined directly from combining two measurements.
Seven years later J. J. Thomson showed that cathode rays consist of streams of particles, to be called electrons, and made more precise measurements of their mass-to-charge ratio again using a cathode ray tube.
With the re-definition of kilogram in 2019, there is no uncertainty by definition left in Planck constant anymore.
The electron relative atomic mass can be measured directly in a Penning trap.
Taking the simplest case of complete ionization of all electrons, for a nuclide X of atomic number Z,[5] As relative atomic masses are measured as ratios of masses, the corrections must be applied to both ions: the uncertainties in the corrections are negligible, as illustrated below for hydrogen 1 and oxygen 16.
The principle can be shown by the determination of the electron relative atomic mass by Farnham et al. at the University of Washington (1995).
[7] It involves the measurement of the frequencies of the cyclotron radiation emitted by electrons and by 12C6+ ions in a Penning trap.
This value is then used to calculate a new approximation to Ar(e), and the process repeated until the values no longer vary (given the relative uncertainty of the measurement, 2.1×10−9): this happens by the fourth cycle of iterations for these results, giving Ar(e) = 5.485799111(12)×10−4 for these data.