Balmer studied the visible spectrum of hydrogen atoms and found that the wavelengths emitted could be described by the following equation

where n = 3, 4, 5 etc. This is now called the Balmer series.

Bohr suggested that the electron in the atom moves in such a way that it possesses 1, 2, 3 etc units of angular momentum (L).

In other words, he suggested that the angular momentum possessed by an electron in an atom is quantised. As an equation this can be written:

From this he showed that the energy, E_n possessed by an electron which has n units of angular momentum, is given by

where k is a constant.

So, the energy  possessed by the electron in the atom is proportional to 1/n² (more detail).

The values of energy given by this equation are called the energy levels of the atom.

Now, if an electron falls from energy level E_initial to level E_final, the energy of the quantum of electro-magnetic radiation emitted will be E = E_final - E_initial.

From Planck’s formula, the energy possessed by a quantum of electro-magnetic radiation is hc/l, therefore

Which has the same form as the Balmer series, if n_final = 2 and

k = R/hc. Thus, the Bohr model of the atom correctly predicts the wavelengths emitted by hydrogen atoms.

Other series in the hydrogen spectrum have been studied by Lyman (U.V.) and Paschen (I.R.).

The Bohr model predicts these series correctly if we put n_final = 1  (for the Lyman series) and n_final = 3  (for the Paschen series).

This diagram shows only the first 3 lines of each series.

The Bohr model of the atom agrees with experiment only for hydrogen atoms: it cannot be applied to more complicated atoms.

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