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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. Its values are natural numbers (from one) making it a discrete variable. Apart from the principal quantum number, the other quantum numbers for bound electrons are the azimuthal ...
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 ...
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 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).
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.
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). [5] [6]
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} .
Orbitals of the Radium. (End plates to [1]) 5 electrons with the same principal and auxiliary quantum numbers, orbiting in sync. ([2] page 364) The Sommerfeld extensions of the 1913 solar system Bohr model of the hydrogen atom showing the addition of elliptical orbits to explain spectral fine structure.