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The magnetic quantum number only affects the electron's energy if it is in a magnetic field because in the absence of one, all spherical harmonics corresponding to the different arbitrary values of are equivalent.
Four quantum numbers can describe an electron energy level in a hydrogen-like atom completely: Principal quantum number (n) Azimuthal quantum number (ℓ) Magnetic quantum number (m ℓ) Spin quantum number (m s) These quantum numbers are also used in the classical description of nuclear particle states (e.g. protons and neutrons).
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 ...
The azimuthal quantum number is the second of a set of quantum numbers that describe the unique quantum state of an electron (the others being the principal quantum number n, the magnetic quantum number m ℓ, and the spin quantum number m s). For a given value of the principal quantum number n (electron shell), the possible values of ℓ are ...
s = spin quantum number; m s = spin magnetic quantum number; ℓ = Azimuthal quantum number; m ℓ = azimuthal magnetic quantum number; j = total angular momentum quantum number; m j = total angular momentum magnetic quantum number
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| to L + S.
For an electron in an orbital with a magnetic quantum number m l, the z-component of the orbital magnetic moment is = which, since g L = 1, is −μ B m l For a finite-mass nucleus, there is an effective g value [ 5 ] g L = 1 − 1 M {\displaystyle g_{L}=1-{\frac {1}{M}}} where M is the ratio of the nuclear mass to the electron mass.
Its values are natural numbers (from one) making it a discrete variable. Apart from the principal quantum number, the other quantum numbers for bound electrons are the azimuthal quantum number ℓ, the magnetic quantum number m l, and the spin quantum number s.