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The principal quantum number is one of four quantum numbers assigned to each electron in an atom to describe the quantum state of the electron. The other quantum numbers for bound electrons are the total angular momentum of the orbit ℓ , the angular momentum in the z direction ℓ z , and the spin of the electron s .
The principal quantum number describes the electron shell of an electron. The value of n ranges from 1 to the shell containing the outermost electron of that atom, that is [ 12 ] n = 1 , 2 , … {\displaystyle n=1,2,\ldots }
The maximum number of electrons in any shell is 2n 2, where n is the principal quantum number. The maximum number of electrons in a subshell is equal to 2(2 l + 1), where the azimuthal quantum number l is equal to 0, 1, 2, and 3 for s, p, d, and f subshells, so that the maximum numbers of electrons are 2, 6, 10, and 14 respectively.
For a given value of the principal quantum number n, the possible values of ℓ range from 0 to n − 1; therefore, the n = 1 shell only possesses an s subshell and can only take 2 electrons, the n = 2 shell possesses an s and a p subshell and can take 8 electrons overall, the n = 3 shell possesses s, p, and d subshells and has a maximum of 18 ...
(typically between 1 eV and 10 3 eV), where R ∞ is the Rydberg constant, Z is the atomic number, n is the principal quantum number, h is the Planck constant, and c is the speed of light. For hydrogen-like atoms (ions) only, the Rydberg levels depend only on the principal quantum number n.
An electron shell is the set of allowed states that share the same principal quantum number, n, that electrons may occupy. In each term of an electron configuration, n is the positive integer that precedes each orbital letter (helium's electron configuration is 1s 2, therefore n = 1, and the orbital contains two electrons).
Therefore, the term with lowest energy is also the term with maximum and maximum number of unpaired electrons with equal spin angular momentum (either +1/2 or -1/2). For a given multiplicity, the term with the largest value of the total orbital angular momentum quantum number has the lowest energy.
The principal quantum number controls the total number of nodal surfaces which is n-1. [31] Loosely speaking, n is energy, ℓ is analogous to eccentricity , and m is orientation. In general, n determines size and energy of the orbital for a given nucleus; as n increases, the size of the orbital increases.