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The principal quantum number was first created for use in the semiclassical Bohr model of the atom, distinguishing between different energy levels. With the development of modern quantum mechanics, the simple Bohr model was replaced with a more complex theory of atomic orbitals .
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 ...
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.
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
is the principal quantum number of the lower energy level, and n 2 {\displaystyle n_{2}} is the principal quantum number of the higher energy level for the atomic electron transition . This formula can be directly applied only to hydrogen-like , also called hydrogenic atoms of chemical elements , i.e. atoms with only one electron being affected ...
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 orbits in which the electron may travel are shown as grey circles; their radius increases as n 2, where n is the principal quantum number. The 3 → 2 transition depicted here produces the first line of the Balmer series, and for hydrogen (Z = 1) it results in a photon of wavelength 656 nm (red light).
If the group is of the [ns, np] type, an amount of 0.85 from each electron with principal quantum number (n–1), and an amount of 1.00 for each electron with principal quantum number (n–2) or less. If the group is of the [d] or [f], type, an amount of 1.00 for each electron "closer" to the nucleus than the group.