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 Δ E by the equation ν=Δ E / h. For hydrogen, the frequencies of the spectral lines are given by ν= cR (1/ n f 2 −1/ n i 2 ) 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