Atomic Structure

ENERGY OF ELECTION

            The electron revolving around the nucleus possesses energy. The total energy of election will be the sum of the kinetic energy and potential energy. i.e.

                                            (1)

            The kinetic energy of the electron is given by:

           
                     
We know that the potential energy of electron can be given by the equation:

            F is the force of attraction between the electron and the nucleus I-e columbic force of attraction given by the equation:
           
 
           
The potential energy can thus be given as under

         
 

      
As the potential energy of electron in the orbit is negative therefore we can write that

              
            Putting values in equation 1 for K.E and P.E

  
                                                           
                   
           
      
                  
           
            We know that

            
                                
    Thus                                                                             
                          
           
             

                                                         
             
                                 (2)
            We know that radius of hydrogen atom is
               
                       
            Putting value of “r” in equation 2 we get
           
              
                       

                (3)

           
            As e, m, , h, are constant therefore they can be separated from equation    (3)

                         (4)

                      
           
           
                Putting values in equation no. (4)

                                                           (5)

           
           
For hydrogen atom the atomic number Z= 1 for   hydrogen equation            (5)

            Can be written as: -

                      
                       
                       
           
            For n= 2

The value of energy differences between adjacent orbits can be calculated as follows:-
           

From the above difference in energy levels we learn that.