Gesamtspinquantenzahl

Gesamtspinquantenzahl refers to the total spin angular momentum of a quantum mechanical system. In atomic physics, it is particularly relevant when considering the spins of electrons within an atom. Each electron possesses an intrinsic angular momentum, called spin, which is quantized and can be either spin-up or spin-down, represented by a spin quantum number of +1/2 or -1/2, respectively. When multiple electrons are present in an atom, their individual spin angular momenta can combine vectorially to form a total spin angular momentum. The total spin quantum number, denoted by S, is a non-negative integer or half-integer that characterizes this combined spin. The possible values of S depend on the number of electrons and their individual spin orientations, often dictated by the Pauli exclusion principle. For a system with N electrons, the total spin quantum number can range from 0 (or 1/2 if N is odd) up to N/2. The resultant total spin angular momentum vector has a magnitude given by sqrt(S(S+1)) * h-bar, where h-bar is the reduced Planck constant. The total spin quantum number plays a crucial role in determining the spectroscopic properties of atoms and molecules, influencing energy levels and selection rules for transitions.