Johann 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. 



Nils 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 quantized. 

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/n^{2} (more detail). 



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

If an electron falls from energy level E_{initial} to
level E_{final}, the energy of the quantum of
electromagnetic radiation emitted will be given by the difference
between these two levels 





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





This equation has the same form as the Balmer series, if
n_{final}=2
and k=h/Rc 

Thus, the Bohr model of the atom correctly predicts the
wavelengths emitted by hydrogen atoms. 



Other series in the hydrogen spectrum have also been
studied 

Lyman measured the wavelengths emitted in the ultraviolet
region and Paschen measured those in the infrared region. 



The Lyman series can be described by the same equation with n_{final}=1
and for the Paschen series, n_{final}=3 



Energy transitions in atoms are often represented by diagrams
similar to the one below, in which the arrows represent electrons
falling from one level to a lower level, each time emitting a
quantum of radiation of a specific wavelength. 







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. 
