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## 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. 