Atomic Structure

ENERGY DIFFERENCE BETWEEN TWO LEVELS

Consider an electron revolving around the nucleus in circular orbit. The electron is with energy  in its energy level  as shown in the figure:

Let suppose the electron absorb energy and jump to a higher energy level  with energy .  As shown in the figures above.

For        and  we can write that

                         

And for  and  we can write that
                       
            
                                                                               
The difference in the energy level is

or
                        

           
This equation gives the difference between the two energy levels
           

DIFFERENCE OF FREQUENCY BETWEEN TWO LEVELS

When an electron jumps from higher energy level with energy  to lower energy level with energy,a quanta a proton of energy is released, which is  equal to  i.e
           
                                  (1)
           
            Equation  (1) can be rearranged as under: -

                                   (2)

As

Therefore

           (3)
           

            This equation 3 shows the frequency of the radiation when electron jump from a higher energy state to the lower energy state.