spectrum: The Quantum Explanation of Spectral Lines

The explanation for exact spectral lines for each substance was provided by the quantum theory. In his 1913 model of the hydrogen atom Niels Bohr showed that the observed series of lines could be explained by assuming that electrons are restricted to atomic orbits in which their orbital angular momentum is an integral multiple of the quantity h/2π, where h is Planck's constant. The integer multiple (e.g., 1, 2, 3 …) of h/2π is usually called the quantum number and represented by the symbol n.

When an electron changes from an orbit of higher energy (higher angular momentum) to one of lower energy, a photon of light energy is emitted whose frequency ν is related to the energy difference ΔE by the equation ν=ΔE/h. For hydrogen, the frequencies of the spectral lines are given by ν=cR (1/n_f²−1/n_i²) where c is the speed of light, R is the Rydberg constant, and n_f and n_i are the final and initial quantum numbers of the electron orbits (n_i is always greater than n_f). The series of spectral lines for which n_f=1 is known as the Lyman series; that for n_f=2 is the Balmer series; that for n_f=3 is the Paschen series; that for n_f=4 is the Brackett series; and that for n_f=5 is the Pfund series. The Bohr theory was not as successful in explaining the spectra of other substances, but later developments of the quantum theory showed that all aspects of atomic and molecular spectra can be explained quantitatively in terms of energy transitions between different allowed quantum states.

Sections in this article:

• Introduction
• The Quantum Explanation of Spectral Lines
• Continuous and Line Spectra

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