Chapter 1st: Atomic Structure and Periodic Table
B.sc 1st year Book
(Page 9)
State and Explain Pauli’s Exclusion Principle
Pauli Exclusion Principle
Pauli (1925) put forward a very important principle that controls the assignment of the values of four quantum numbers of an electron in an atom. it applies certain restrictions on their values for electrons hence the name “Exclusion principle“. This principle it will be stated as :
‘No two Electrons(e) have all the four (4) quantum values identical’
(As no two individuals of our society can have the same name, father’s name, Vill or Moh. and Post office)
Or No two electrons(e) of an atom can exist in the same quantum state.
Or No two electrons(e) of an atom can exist in the same quantum state.
The statements given above are identical and carry the same meaning that if two electrons of an atom have the same values of principal quantum number ‘n‘ azimuthal quantum number ‘l’ and magnetic quantum number, ‘m‘, they must have different values of spin quantum number. ‘s‘. Thus, every electron in any atom differs from the other in total energy.
Thus, according to Pauli’s principle the electrons entering the same orbital should have opposite spins as shown below:
Thus, according to Pauli’s principle the electrons entering the same orbital should have opposite spins as shown below:
↑↓ 
Anti Parallel spins
(Thermodynamically Very Stable) 
↓↓  ∞  ↑↑ 
Parallel spins
(Thermodynamically Very UnStable) 
Because the state of opposite spins (↑↓) gives a lower energy state and provides extra stability than when pairing of electrons with parallel spins (↑↑) or (↓↓).
From the above discussion, it is concluded that an orbital never contains electrons of the same spin.
Explain Pauli Exclusion Principle
On comparing the quantum number values of any two electrons of the same shell or of different shells of an atom; we find that no two electrons can have all four quantum number values identical. Maximum any three quantum number values for two electrons may be the same but the remaining one must be different. Thus, Pauli’s exclusion principle is strictly followed.
Shell  Electron number  Quantum Number  Total electrons 
K 

 Two 
L 
3rd
and so on. 
 Eight 
Comparison between the electrons : 
For 1st and 2nd  n, I, and m values are the same, and s values are different 
For 1st and 3rd  I, m, and s are the same but n values are different 
For 2nd and 3rd  I, m, and s are the same, and n and s values are different 
For 3rd and 4th  n, I, and m values are the same, and s values are different 
For 3rd and 5th  n and s values are the same, but I and m values are different 
Related Topic  Atomic Structure and Periodic Table 
Importance of Pauli’s Exclusion Principle.
(i) This principle is very much useful in determining the maximum number of electrons In each principal level or subenergy level by the following equation :
A total number of electrons (e) in the main energy level :
$$ \sum _{f=0}^{l\left(n1\right)}2\left(2I\:+1\right)=2n^2 $$
Where n = principal quantum number and
l = Azimuthal quantum number(AQN). Thus, putting ‘n‘ and ‘l‘ values in the above formula. we can calculate the total number of electrons possible in the arty shell.
For example: For K shell
Total number of electrons,
$$ \sum _{f=0}^{l\left(n1\right)}2\left(2I\:+1\right)=2\times \left(2\times 0+1\right)=2\times 1=2 $$
For L shell
Total number of electrons,
$$ \sum _{f=0}^{l\left(n1\right)}2\left(2I\:+1\right)=2\times \left(2\times 0+1\right)+2\times \:\left(2\times \:1+1\right)=2\times 1+2\times 3=8 $$
Total number of electrons
Thus, the total number of electrons in each shell is equal to 2n^{2}.
(ii) The other remarkable importance of this principle is to decide the preferred arrangements of electrons in an orbital.
(iii) Why are the orbital not contain more than two electrons? can reasonably explain by using Pauli’s exclusion principle.
Frequently Asked Questions
Pauli Exclusion Principle:Paulis exclusion principle is said that in atom. There are no any two or more atom are identical. It have must a different in (n) Principal Quantum Number, (l) Azimuthal Quantum Number, (m) magnetic quantum number or (s) Spin Quantum Number
Pauli (1925) put forward a most important principle that controls the assignment of the values of 4 quantum numbers of an electron(e^{–}) in an atom. it applies certain restrictions/barriers on their values for electrons(e^{–}) hence the name “Exclusion principle“.