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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 four quantum numbers n, ℓ, m, and s specify the complete and unique quantum state of a single electron in an atom, called its wave function or orbital. Two electrons belonging to the same atom cannot have the same values for all four quantum numbers, due to the Pauli exclusion principle .
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 (m l or m [a]) distinguishes the orbitals available within a given subshell of an atom.
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 = 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 principal quantum number (n) is shown at the right of each row. In quantum mechanics, the azimuthal quantum number ℓ is a quantum number for an atomic orbital that determines its orbital angular momentum and describes aspects of the angular shape of the orbital.
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 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 ...