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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 .
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]
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 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} .
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 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).
A hydrogen-like atomic orbital is uniquely identified by the values of the principal quantum number n, the angular momentum quantum number l, and the magnetic quantum number m. The energy eigenvalues do not depend on l or m, but solely on n. To these must be added the two-valued spin quantum number m s = ± 1 ⁄ 2, setting the stage for the ...
The dihydrogen cation or hydrogen molecular ion is a cation (positive ion ... potential due to rotation with angular momentum described by the quantum number L. The ...