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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.
In quantum physics and chemistry, quantum numbers are quantities that characterize the possible states of the system. To fully specify the state of the electron in a hydrogen atom, four quantum numbers are needed. The traditional set of quantum numbers includes the principal, azimuthal, magnetic, and spin quantum numbers. To describe other ...
In what follows, B is an applied external magnetic field and the quantum numbers above are used. Property or effect Nomenclature Equation orbital magnetic dipole moment:
The boxes represent different magnetic quantum numbers. As an example, consider the ground state of silicon . The electron configuration of Si is 1s 2 2s 2 2p 6 3s 2 3p 2 (see spectroscopic notation ).
where 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.
The quantum numbers corresponding to these operators are , , (always 1/2 for an electron) and respectively. The energy levels in the hydrogen atom depend only on the principal quantum number n . For a given n , all the states corresponding to ℓ = 0 , … , n − 1 {\displaystyle \ell =0,\ldots ,n-1} have the same energy and are degenerate.
The integer m (not to be confused with the moment, ) is called the magnetic quantum number or the equatorial quantum number, which can take on any of 2j + 1 values: [20], (), , , , +, , + (), + . Due to the angular momentum, the dynamics of a magnetic dipole in a magnetic field differs from that of an electric dipole in an electric field.
The magnetic quantum number m is an integer satisfying −ℓ ≤ m ≤ ℓ, so for every n and ℓ there are 2ℓ + 1 different quantum states, labeled by m. Thus, the degeneracy at level n is ∑ l = … , n − 2 , n ( 2 l + 1 ) = ( n + 1 ) ( n + 2 ) 2 , {\displaystyle \sum _{l=\ldots ,n-2,n}(2l+1)={(n+1)(n+2) \over 2}\,,} where the sum ...