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The electron is a charged particle with charge − e, where e is the unit of elementary charge. Its angular momentum comes from two types of rotation: spin and orbital motion. From classical electrodynamics, a rotating distribution of electric charge produces a magnetic dipole, so that it behaves like a tiny bar magnet.
The Weiss magneton was experimentally derived in 1911 as a unit of magnetic moment equal to 1.53 × 10 −24 joules per tesla, which is about 20% of the Bohr magneton. In the summer of 1913, the values for the natural units of atomic angular momentum and magnetic moment were obtained by the Danish physicist Niels Bohr as a consequence of his ...
where N is the Avogadro constant, g is the Landé g-factor, and μ B is the Bohr magneton. In this treatment it has been assumed that the electronic ground state is not degenerate, that the magnetic susceptibility is due only to electron spin and that only the ground state is thermally populated.
The magnetic moment of the electron is =, where μ B is the Bohr magneton, S is electron spin, and the g-factor g S is 2 according to Dirac's theory, but due to quantum electrodynamic effects it is slightly larger in reality: 2.002 319 304 36.
The Hamiltonian for an electron in a static homogeneous magnetic field in an atom is usually composed of three terms = + (+) + where is the vacuum permeability, is the Bohr magneton, is the g-factor, is the elementary charge, is the electron mass, is the orbital angular momentum operator, the spin and is the component of the position operator orthogonal to the magnetic field.
The magnetic moment would later be explained in quantum theory by the Bohr magneton (), which is used in the Brillouin function. It could be noted that there is a difference in the approaches of Langevin and Bohr, since Langevin assumes a magnetic polarization μ {\displaystyle \mu } as the basis for the derivation, while Bohr start the ...
In order to solve the equation of an electron in a spherical potential, Hartree first introduced atomic units to eliminate physical constants. Then he converted the Laplacian from Cartesian to spherical coordinates to show that the solution was a product of a radial function () / and a spherical harmonic with an angular quantum number , namely = (/) (,).
Here the small corrections to the relativistic result g = 2 come from the quantum field theory calculations of the anomalous magnetic dipole moment. The electron g -factor is known to twelve decimal places by measuring the electron magnetic moment in a one-electron cyclotron: [ 3 ] g e = − 2.002 319 304 361 18 ( 27 ) . {\displaystyle g ...