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The Bohr Model of the Hydrogen Atom (1)
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, En 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.  
If an electron falls from energy level Einitial to level Efinal, the energy of the quantum of electro-magnetic radiation emitted will be given by the difference between these two levels  
 
   
From Planck’s formula, the energy possessed by a quantum of electro-magnetic radiation is hc/l, therefore  
 
   
This equation has the same form as the Balmer series, if  nfinal=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 ultra-violet region and Paschen measured those in the infra-red region.  
   
The Lyman series can be described by the same equation with nfinal=1 and for the Paschen series, nfinal=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.  
 
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