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 n^{2}
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,(n1) ,
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
subshells or subshells.
·
No of subshells = value of n
If n= 1
then 1 subshell = (l=0)
If n= 2
then 2 subshell = (l=0,1)
If n= 3
then 3 subshell = (l=0,1,2)
·
Value of l =
0, 1, 2,
3, 4, 5 
Notation for subshell= s, p, d, f, g,
h
·
Subshell notation
n

l

Subshell
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 ‘m_{i}’
·
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

Subshell
notation

S

P

D

F

G

H

No of orbital’s

1

3

5

7

9

11

Electron Spin Quantum Number (m_{s})
·
Proposed by G. Uhlen beck & S.
Goodsmit (1925)
·
Electrons spins around its own axis
·
M_{s }have two value +1/2 &
1/2
·
M_{s} gives information about
orientation of the spin of the
electron.
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