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In quantum mechanics, the principal quantum number (symbolized n) is one of four quantum numbers assigned to each electron in an atom to describe that electron's state.
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 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.
The Balmer series is characterized by the electron transitioning from n ≥ 3 to n = 2, where n refers to the radial quantum number or principal quantum number of the electron. The transitions are named sequentially by Greek letter: n = 3 to n = 2 is called H-α, 4 to 2 is H-β, 5 to 2 is H-γ, and 6 to 2 is H-δ.
The principal quantum number in hydrogen is related to the atom's total energy. Note that the maximum value of the angular momentum quantum number is limited by the principal quantum number: it can run only up to n − 1 {\displaystyle n-1} , i.e., ℓ = 0 , 1 , … , n − 1 {\displaystyle \ell =0,1,\ldots ,n-1} .
(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.
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.
Z is the atomic number, n′ (often written ) is the principal quantum number of the lower energy level, n (or ) is the principal quantum number of the upper energy level, and; is the Rydberg constant. (1.096 77 × 10 7 m −1 for hydrogen and 1.097 37 × 10 7 m −1 for heavy metals).