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.

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:

 ↑↓ 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 1st2nd n=1, I=0, m=0, s= +1/2n=1, I=0, m=0, s= -1/2 Two L 3rd4th5th6th7th8th9th10thand so on. n=2, I=0, m=0, s= +1/2n=2, I=0, m=0, s= -1/2n=2, I=1, m=1, s= +1/2n=2, I=1, m=0, s= +1/2n=2, I=1, m=+1, s= +1/2n=2, I=1, m=+1, s= +1/2n=2, I=1, m=1, s= -1/2n=2, I=0, m=0, s= -1/2n=2, 1=0, m=+1, s= -1/2 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

 Bohr’s Atomic Model De Broglie Hypothesis De Broglie Equation Heisenberg uncertainty Principle Schrodinger Wave Equation Shapes of orbitals Quantum Numbers Hunds Rule Pauli Exclusion Principle Energy level diagram of Atom Aufbau Principle Screening effect or shielding effect Periodic Table Moseley Periodic law Classification of elements

## 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 sub-energy level by the following equation :

A total number of electrons (e) in the main energy level :

$$\sum _{f=0}^{l-\left(n-1\right)}2\left(2I\:+1\right)=2n^2$$

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,

$$\sum _{f=0}^{l-\left(n-1\right)}2\left(2I\:+1\right)=2\times \left(2\times 0+1\right)=2\times 1=2$$

For L shell

Total number of electrons,

$$\sum _{f=0}^{l-\left(n-1\right)}2\left(2I\:+1\right)=2\times \left(2\times 0+1\right)+2\times \:\left(2\times \:1+1\right)=2\times 1+2\times 3=8$$

### Total number of electrons

Thus, the total number of electrons in each shell is equal to 2n2.

(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.