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Each energy level, or electron shell, or orbit, is designated by an integer, n as shown in the figure. The Bohr model was later replaced by quantum mechanics in which the electron occupies an atomic orbital rather than an orbit, but the allowed energy levels of the hydrogen atom remained the same as in the earlier theory.
The energy levels of hydrogen, including fine structure (excluding Lamb shift and hyperfine structure), are given by the Sommerfeld fine-structure expression: [13] = [(+ [+ (+)]) /] [+ (+)], where is the fine-structure constant and is the total angular momentum quantum number, which is equal to | |, depending on the orientation of the electron ...
The Bohr model of the hydrogen atom (Z = 1) or a hydrogen-like ion (Z > 1), where the negatively charged electron confined to an atomic shell encircles a small, positively charged atomic nucleus and where an electron jumps between orbits, is accompanied by an emitted or absorbed amount of electromagnetic energy (hν). [1]
This equation is obtained from combining the Rydberg formula for any hydrogen-like element (shown below) with E = hν = hc / λ assuming that the principal quantum number n above = n 1 in the Rydberg formula and n 2 = ∞ (principal quantum number of the energy level the electron descends from, when emitting a photon).
The energy levels in the hydrogen atom depend only on the principal quantum number n. For a given n , all the states corresponding to ℓ = 0 , … , n − 1 {\displaystyle \ell =0,\ldots ,n-1} have the same energy and are degenerate.
In atomic physics, hyperfine structure is defined by small shifts in otherwise degenerate electronic energy levels and the resulting splittings in those electronic energy levels of atoms, molecules, and ions, due to electromagnetic multipole interaction between the nucleus and electron clouds.
Computed energy level spectrum of hydrogen as a function of the electric field near n = 15 for magnetic quantum number m = 0. Each n level consists of n − 1 degenerate sublevels; application of an electric field breaks the degeneracy. Energy levels can cross due to underlying symmetries of motion in the Coulomb potential.
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).