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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).
In Bohr's theory describing the energies of transitions or quantum jumps between orbital energy levels is able to explain these formula. For the hydrogen atom Bohr starts with his derived formula for the energy released as a free electron moves into a stable circular orbit indexed by : [28] = The energy difference between two such levels is ...
Depiction of a hydrogen atom showing the diameter as about twice the Bohr model radius. (Image not to scale) A hydrogen atom is an atom of the chemical element hydrogen.The electrically neutral hydrogen atom contains a single positively charged proton in the nucleus, and a single negatively charged electron bound to the nucleus by the Coulomb force.
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 associated to an electron is that of its orbital. The energy of a configuration is often approximated as the sum of the energy of each electron, neglecting the electron-electron interactions. The configuration that corresponds to the lowest electronic energy is called the ground state. Any other configuration is an excited state.
Relativistic corrections (Dirac) to the energy levels of a hydrogen atom from Bohr's model. The fine structure correction predicts that the Lyman-alpha line (emitted in a transition from n = 2 to n = 1) must split into a doublet. The total effect can also be obtained by using the Dirac equation.
The Bohr radius ( ) is a physical constant, approximately equal to the most probable distance between the nucleus and the electron in a hydrogen atom in its ground state. It is named after Niels Bohr, due to its role in the Bohr model of an atom. Its value is 5.291 772 105 44 (82) × 10 −11 m. [1] [2]
This formula indicated the existence of an infinite series of ever more closely spaced discrete energy levels converging on a finite limit. [6] This series was qualitatively explained in 1913 by Niels Bohr with his semiclassical model of the hydrogen atom in which quantized values of angular momentum lead to the observed discrete energy levels.