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Principal quantum number
noun
The quantum number (of an atomic orbital) that specifies the energy of an electron in an atom and, hence, which shell it occupies
Exact(37)
The principal quantum number is an integer n that corresponds to the gross energy states of the atom.
For principal quantum number 1 there is but a single type of orbital, called an s orbital.
It follows from the allowed values of l that there are n subshells in a shell of principal quantum number n.
The number l, called the orbital quantum number, must be less than the principal quantum number n, which corresponds to a "shell" of electrons.
As the principal quantum number increases, there are an increasing number of different types of orbitals, or subshells, corresponding to each: s, p, d, f, g, etc.
Each shell consists of n2 individual orbitals with the same principal quantum number and hence (in the hydrogen atom) the same energy.
Similar(23)
Typically, the fine structure is on the order of one-millionth of the energy difference between the energy levels given by the principal quantum numbers.
Here, we assume that energy eigenvalues are well approximated by those of the hydrogen atom for smaller principal quantum numbers.
It may correspond to transitions between energy bands with principal quantum numbers that are equal to 2. The physical nature of excitation is inessential for further calculations, but further it will be shown that their nature may be determined experimentally.
a For circular orbits, the lowest ones in each atomic shells – including the valence ones, one has ΔO=Δr=2πr, with r the orbital radii thereof, while O=p is the fixed particle's momentum on that orbit; therefore, when combined into eq. (18b) they provide the celebrated Bohr-de Broglie relationship rp=nħ solving the atomic spectra of Hydrogen atom in principal quantum numbers (n).
Thus, l divides each shell into n subshells consisting of all electrons of the same principal and orbital quantum numbers.
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