- According to Pauli's exclusion principle, no two electrons can occupy the same quantum state, defined by the four quantum numbers n, l, ml, and ms. - The principle determines the maximum number of electrons that can occupy each atomic shell and subshell. For example, the K shell (n=1) can hold up to 2 electrons, while the L shell (n=2) can hold up to 8 electrons distributed between its s and p subshells. - Electrons fill atomic orbitals following a set order based on minimizing energy: 1s, 2s, 2p, 3s, 3p, 4s, etc. This determines the electronic configuration that represents the distribution of electrons

2.  Guided by
 Gyanrav dhoty
 Presented by
 Pooja sharma
 B.Sc.5th sem(c.s)

3. Topic –pauli’s exclusion principle

4.  According to pauli’s exclusion principle,the state of electron in
an atom is expressed by the four quantum numbers n,l,ml ms
and in an atom there can be no two eletrons in the same
quantum state i.e. all the four quantum number n,l,ml ms can
not be the same for two eletrons.
 FRom the above principle,it is clear that
 1.For n=1(k shell),l=0,ml=0,ms=_1/2 and+1/2.
 Hence,there are the following two quantum states possible
for the values of n,l,ml and ms:
 (1,0,0,_1/2) and(1,0,0,+1/2)
 Thu there can not be more than two electrons in the k shell
i.e.,maximum number of electrons in the k shell=2

5.  For n=2 (L shell) l=0 and 1
 For l=0,ml=0 and
 for l=1 ml=-1,0,+1 and ms=-1/2 and +1/2
 Hence there are following 8 possible quantum
state of n,l,ml and ms possible:
 (2,0,0,-1/2) (2,0,0,+1/2) (2,1,-1,-1/2) (2,1,-
1,+1/2) (2,1,0,-1/2) (2,1,0,+1/2) (2,1,1,-1/2)
(2,1,-1,+1/2)
 Thu there can be maximum 8 electron in the L
shell.

6.  From the above discussion , in general we can say
that there are constant values of n and l for a sub
shell , for a given value of l , there are total (2l+ 1)
values of me and for each value of ml, there are two
possible values of
Ms (-½ and + ½ ) Hence maximum namber of
Electrons in a sub shel = 2 (2l+1)-(1)
for each shell , the value of nis constant bul l con
have different
value . For a given value of n, there are total n
integer possibale values of l from o to (n-1). Hence


7. Maximum number of Electrons in Nth shells
n-1
= ∑2(2l+1) =2[ 1+3+S+1+…..+(2n-1)]
l=0
= 2[ n/2{ 1+(2n-1)}]= 2n²………(іі)
The maximum number of electrons in Diffrwnt
Shells and sub sells is given in the follow in
table

9.  According to pauli’s exclusion principle,there
can not be two or more than two electrons in
a shell or sub-shell in the same quantum
state(which is determinded by the quantum
numbers n,l ml and ms)
 Since each system has a tendency to be in the
lowest energy state ,therefore first the s sub-
shell of k shell is filled up by the eletrons and
then the s sub-shell of L shell,then p sub-
shell of L shell,and so. on.

10. the order of filling the different sub-shells
by the electrons is as
follows:1s,2s,2p,3s,3p,4s,3d,4p,5s,4d,5p,6s,
4f,5d,6p,7s,5f,6d,7p.

11.  To represent the eletronic configuration of
eletrons in an atoms,
For example,in sodim atom(z=11) out of
11eietrons,2 electrons are in s sub-shell of k
shell(n=1),2 electrons are in s sub-shell of L
shell (n=2) ,6 electrons are in p sub-shell
distribution of electrons is represented as
below:
1s²,2s²,2p6,3s1 .