General Properties of the Electron

Elementary particles exhibit a wave and a particle nature depending on the specific experiment. Owing to its relatively small rest energy E0 = m_ec² ≈ 0.51 MeV, the electron approaches roughly half the speed of light c ≈ 3 ˟ 10⁸ms⁻¹ at an accelerating voltage U ≈ 60kV. Therefore, it is necessary to consider relativistic effects for accelerating voltages larger than about 100 kV. Despite the fact that we can consider the electron as a point-like particle, it has an angular momentum associated with a magnetic moment:

$$\mu = \frac{{eg\mu _0 }}{{2m_e }}s = \frac{{e\mu _0 \hbar }}{{2m_e }}$$

(1)

Here, e and ħ are the charge of the electron and the Planck constant, respectively;μ₀ is the permeability of the vacuum. We use SI units, which now are universally accepted. From the point of view of classical electrodynamics, a magnetic moment originates from a rotating charge of finite extension forming a magnetic dipole. However, the measured ratio of the magnetic moment and the angular momentum or spin s = ħ/2 of the electron is twice as large as predicted by classical electrodynamics. This discrepancy, which requires an empirical Lande factor g = 2, can only be explained by means of the relativistic electron theory of Dirac [35, 36]. The spin s of the electron is comparable with the polarization of the light.