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.