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An electron's angular momentum, L, is related to its quantum number ℓ by the following equation: = (+), where ħ is the reduced Planck constant, L is the orbital angular momentum operator and is the wavefunction of the electron.
Quantum orbital motion involves the quantum mechanical motion of rigid particles (such as electrons) about some other mass, or about themselves.In classical mechanics, an object's orbital motion is characterized by its orbital angular momentum (the angular momentum about the axis of rotation) and spin angular momentum, which is the object's angular momentum about its own center of mass.
Each orbital in an atom is characterized by a set of values of three quantum numbers n, ℓ, and m ℓ, which respectively correspond to electron's energy, its orbital angular momentum, and its orbital angular momentum projected along a chosen axis (magnetic quantum number). The orbitals with a well-defined magnetic quantum number are generally ...
This would ultimately become the quantized values of the projection of spin, an intrinsic angular momentum quantum of the electron. In 1927 Ronald Fraser demonstrated that the quantization in the Stern-Gerlach experiment was due to the magnetic moment associated with the electron spin rather than its orbital angular momentum. [7]
, the magnitude of the angular momentum in the -direction, is given by the formula: [7] L z = m l ℏ {\displaystyle L_{z}=m_{l}\hbar } . This is a component of the atomic electron's total orbital angular momentum L {\displaystyle \mathbf {L} } , whose magnitude is related to the azimuthal quantum number of its subshell ℓ {\displaystyle \ell ...
In atomic physics, a term symbol is an abbreviated description of the total spin and orbital angular momentum quantum numbers of the electrons in a multi-electron atom.So while the word symbol suggests otherwise, it represents an actual value of a physical quantity.
Interferometric methods borrowed from light optics also work to determine the orbital angular momentum of free electrons in pure states. Interference with a planar reference wave, [5] diffractive filtering and self-interference [15] [16] [17] can serve to characterize a prepared electron orbital angular momentum state. In order to measure the ...
If the electron is visualized as a classical rigid body in which the mass and charge have identical distribution and motion that is rotating about an axis with angular momentum L, its magnetic dipole moment μ is given by: =, where m e is the electron rest mass. The angular momentum L in this equation may be the spin angular momentum, the ...