Atomic Structure

QUANTUM NUMBERS
            According to the wave theory electron revolve around nucleus in shell. It also explains that there are not any shells but also sub-shells or sub-energy level. In order to locate the orbital or energy level of an electron, we require four quantum numbers. Three of them are obtained from the solution of wave theory. The fourth quantum number is the spin quantum number describing the spin of electron in the orbit.
The four quantum numbers are as under
            i)          Principal Quantum Number    (n )
            ii)         Azimuthall Quantum Number  (l)

1)         PRINCIPLE QUANTUM NUMBER (n): 
            Principal quantum number shows the main energy level or shell of an electron. It is represented by “n” it also shows the total number of electron present in an energy  shell. If the value of ”n” is greater, it show that the electron is away from the nucleus. If value of “n” in smaller, then the electron  will be nearer to nucleus.
            The potential energy of electron will be greater, if the value of n is greater and electron will be away from the nucleus.
            Maximum number of electron in an energy shell can be calculated by 2n2:
Principal Quantum number (n): 1       2          3          4          4          5          6         
Letter designation:                       K     L          M         N          O         P          Q
Number of electrons:          2     8         18        32        -           -           -          
2)         AZIMUTHAL QUANTUM NUMBER(l):
            This quantum number can also be called as sub energy level or shell or secondary quantum number. This quantum number is denoted by (l). The Azimuthal quantum number shows the number of sub energy shell present in main shell which is denoted by ”n“ The Azimuthal quantum number also describe the shape of the orbital (sub-energy level). The value of l varies from 0 to n-1 . It means that if the value of n= 1
            Then Azimuthal quantum number l=n-1=1-1=0
and if n=2
Then l =n-1= 2-1 =1
            The sub shell present in the main shell are also represented by letters s,p,d and f. where s stands for shape, p for principal, d for  diffused and f for fundamental. The s sub shell is lowest in energy. The energy for these sub-shell increases from s to f. Thus energy wise.
                        s<p<d<f.
            The sub shell s is spherical in shape.
            The sub-shell p is dumb bell in shape.
            The sub- shell d is double dub bell is shape.
            The shape of “f” sub- shell in very complicated and cannot be drawn.
            For an atom we can generally say that
           if principal quantum No, n=            1,   2,   3,   4
then aumuthal quantum No  l = (n-1) = 0,   1,  2,    3,
The sub shell present will be  =              s,   p,  d,    f

            As it is clear that the atoms possess, main shell.  Each main shell has one or more sub-shells and each sub shell has orbital.
            The magnetic quantum number shows the number of orbital present in the sub-shell. The magnetic quantum number denoted by shows the orientation of orbital in space present in a sub-shell. It also explains the direction of orbital if it is placed in a magnetic field.
            The value of magnetic quantum number changes from negative to positive. Each value indicates a specific orbital. Each orbital can place only two electro at maximum. The number of orbital present in a sub- shell is obtained by (2l+1). Thus we can suggest that if.
Principle quantum No  ”n”       1          2          3          4          5
Letter designation                   k          L          M         N          O        
Arimuthal Q.No                       O         1          2          3          4
Sub shell                                 S          P          D         F         
No of orbital in sub shell(2l+1)1          3          5          7
Number of orbital in sub shell
Total number of orientations I-e the magnetic quantum number (ml) for each sub- shell can b written as under:
 

4.         SPIN QUANTUM NUMBER     Electron revolves around the nucleus. This electron revolves around its own axis also. This revolution is described by the spin quantum number. Spin quantum number is represented by ms.
            The revolution or spinning of electron around its axis can be clockwise or anticlockwise. If it is clockwise it is denoted by (↑) and is given +1/2 value of . If it is anticlockwise it is denoted by (↓) and is given -1/2 value of.  When two electrons occupy the same orbital  in a sub-shell. They will have opposite spin. It means that one electron will spin with +1/2 value and other with -1/2 value of . Both electrons in the orbit are represented by (↑↓) showing opposite spin.

              The above discussion about the four quantum numbers can be summarized in the following table.