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Magnetic quantum number. In atomic physics, a magnetic quantum number is a quantum number used to distinguish quantum states of an electron or other particle according to its angular momentum along a given axis in space. The orbital magnetic quantum number (ml or m[ a ]) distinguishes the orbitals available within a given subshell of an atom.
The magnetic quantum number describes the specific orbital within the subshell, and yields the projection of the orbital angular momentum along a specified axis: L z = m ℓ ħ The values of m ℓ range from − ℓ to ℓ , with integer intervals.
For example, the "4s subshell" is a subshell of the fourth (N) shell, with the type (s) described in the first row. The second column is the azimuthal quantum number (ℓ) of the subshell. The precise definition involves quantum mechanics, but it is a number that characterizes the subshell.
The first dictates that no two electrons in an atom may have the same set of values of quantum numbers (this is the Pauli exclusion principle). These quantum numbers include the three that define orbitals, as well as the spin magnetic quantum number m s. Thus, two electrons may occupy a single orbital, so long as they have different values of m s.
Term symbol. 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. For a given electron configuration of an atom, its state depends ...
Hund's first rule states that the lowest energy atomic state is the one that maximizes the total spin quantum number for the electrons in the open subshell. The orbitals of the subshell are each occupied singly with electrons of parallel spin before double occupation occurs.
Let's say we want to calculate transition dipole moments for an electron transition from a 4d to a 2p orbital of a hydrogen atom, i.e. the matrix elements of the form , | |, , where r i is either the x, y, or z component of the position operator, and m 1, m 2 are the magnetic quantum numbers that distinguish different orbitals within the 2p or 4d subshell.
Azimuthal quantum number. The atomic orbital wavefunctions of a hydrogen atom: The azimuthal quantum number (ℓ) is denoted by letter at the top of each column. The principal quantum number (n) is shown at the right of each row. In quantum mechanics, the azimuthal quantum numberℓ is a quantum number for an atomic orbital that determines its ...