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.