Quantum Mechanical Model of Atom :: Principle Quantum Number ‘n’ , Azimuthal Quantum Number ‘p’ , Magnetic Orbital Quantum Number ‘mi’ , and Electron Spin Quantum Number (ms)

Quantum Mechanical Model of Atom

Branches of science which explain duel behavior of Metter is called quantum mechanics .
ð Quantum mechanics independently developed by Werner Heisenberg and Erwin Schrodinger (1926)
Fundamental equation developed by Schrodinger (won Nobel Prize 1933)
Equation for a system (atom or molecules was energy does not change with time)

Principle Quantum Number ‘n’

·        It is a positive Integer with value of n = 1,2,3……
·        It determine size and energy of orbital
·        It also identifies the shell with increase in an , number of allowed orbital increase. And given by n2
N      =1,    2,    3,    4……..
Shell = k,    l,    m,    l……
·        Size of orbital increase with increase in an  n.

             Azimuthal Quantum Number ‘p’

·        It is also known as orbital angular momentum or subsidiary quantum no.
·        It defined 3d shape of orbital of orbital
·        For given value of n possible value of  
        L= 0,1,2,3,4,5,———-(n-1) ,
                    Ex :- if   n=1   then   l=0
                             if   n=2   then   l=0,1
                             if   n=5   then   l=0,2,3,4
·        Each shell consists of one or more sub-shells or sub-shells.
·        No of sub-shells = value of  n
If  n= 1  then  1 sub-shell =  (l=0)
If  n= 2  then  2 sub-shell =  (l=0,1)
If  n= 3  then  3 sub-shell =  (l=0,1,2)
·                      Value of    l =  0,  1,  2,  3,  4,  5  ———-
     Notation for sub-shell= s, p, d,   f,   g, h————–
·        Sub-shell notation
n
l
Sub-shell   notation
1
0
1s
2
0
2s
2
1
2p
3
0
3s
3
1
3p
3
2
3d
4
0
4s
4
1
4p
4
2
4d
4
3
4f

 Magnetic Orbital Quantum Number ‘mi

·        This quantum no (mi) gives information about orientation of  the  orbital .
·        Ml = (2l+1) i.e. if value of   l  is  1 then value of  ml = 2×1+1=3=(-1,0,1)
Value of p
0
1
2
3
4
5
Sub-shell notation
S
P
D
F
G
H
No of orbital’s
1
3
5
7
9
11

Electron Spin Quantum Number (ms)

·        Proposed by G. Uhlen beck & S. Goodsmit (1925)
·        Electrons spins around its own axis
·        Ms have two value +1/2 & -1/2
·        Ms gives information about orientation of the spin of   the electron.

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