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The phrase spin quantum number refers to quantized spin angular momentum. The symbol s is used for the spin quantum number, and m s is described as the spin magnetic quantum number [3] or as the z-component of spin s z. [4] Both the total spin and the z-component of spin are quantized, leading to two quantum numbers spin and spin magnet quantum ...
S is the total spin quantum number for the atom's electrons. The value 2S + 1 written in the term symbol is the spin multiplicity, which is the number of possible values of the spin magnetic quantum number M S for a given spin S. J is the total angular momentum quantum number for the atom's electrons. J has a value in the range from |L − S ...
The spin magnetic quantum number m s specifies the z-axis component of the spin angular momentum for a particle having spin quantum number s. For an electron, s is 1 ⁄ 2 , and m s is either + 1 ⁄ 2 or − 1 ⁄ 2 , often called "spin-up" and "spin-down", or α and β.
A quantum number beginning in n = 3,ℓ = 0, describes an electron in the s orbital of the third electron shell of an atom. In chemistry, this quantum number is very important, since it specifies the shape of an atomic orbital and strongly influences chemical bonds and bond angles. The azimuthal quantum number can also denote the number of ...
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.
The associated quantum number is the main total angular momentum quantum number j. It can take the following range of values, jumping only in integer steps: [ 1 ] | ℓ − s | ≤ j ≤ ℓ + s {\displaystyle \vert \ell -s\vert \leq j\leq \ell +s} where ℓ is the azimuthal quantum number (parameterizing the orbital angular momentum) and s is ...
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.
Rotating a spin-2 particle 180° can bring it back to the same quantum state, and a spin-4 particle should be rotated 90° to bring it back to the same quantum state. The spin-2 particle can be analogous to a straight stick that looks the same even after it is rotated 180°, and a spin-0 particle can be imagined as sphere, which looks the same ...