Stability of Fully Filled and Half Filled Orbitals: Factors Affecting Stability, Examples, Practice Problems & FAQs

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Table of contents

Factors affecting the stability of fully and half-filled orbitals
Exchange energy
Symmetricity
Practice problems
Frequently asked questions-FAQs

Factors affecting the stability of fully and half-filled orbitals

The factors mainly affecting the stability of half-filled and fully filled orbitals are

Exchange energy
Symmetricity

Exchange energy

Electrons having the same spin and energy present in degenerate orbitals can exchange their positions and in this exchange process, the energy is released and the released energy is termed exchange energy.

The higher the number of exchanges in a particular configuration, the stability of the configuration becomes higher.

The exchange energy is the basis for Hund's rule, which allows maximum multiplicity, that is electron pairing is possible only when all the degenerate orbitals contain one electron each.

more the number of exchange ∝ more the stability of configuration

$\Rightarrow m a x i m u m n u m b e r o f p o s s i b l e e x c h a n g e = C_{r}^{n} = \frac{n!}{r! (n - r)!}$

Where n is the total number of electrons having same energy and spin

r = 2 (minimum 2 electrons required for exchange)

Symmetricity

Nature likes symmetry. Symmetry leads to stability. Fulfilled and half-filled subshells are symmetrical. So, they are more stable.

Half filled subshells:

Fully filled subshells:

Due to the symmetrical distribution of electrons in degenerated orbitals (having different orientations), having less shielding with respect to others and electrons attracted more towards the nucleus, hence increasing stability.

Practice problems:

Q 1. Calculate the number of maximum possible exchanges in configuration d5?

Answer: (A)

Solution:

d5 configuration:

Number of electrons having same energy and spin (n) = 5

Minimum number of electrons required for exchange = 2

$\Rightarrow m a x i m u m n u m b e r o f p o s s i b l e e x c h a n g e = C_{r}^{n} = \frac{n!}{r! (n - r)!}$

$\Rightarrow m a x i m u m n u m b e r o f p o s s i b l e e x c h a n g e = C_{2}^{5} = \frac{5 \times 4}{2 \times 1} = 10$

Q 2. Calculate the number of maximum possible exchanges in configuration d8?

Answer: (C)

Solution:

d8 configuration:

Case 1:

Number of electrons having same energy and spin (n) = 5

Minimum number of electrons required for exchange = 2

$\Rightarrow m a x i m u m n u m b e r o f p o s s i b l e e x c h a n g e = C_{r}^{n} = \frac{n!}{r! (n - r)!}$

$\Rightarrow m a x i m u m n u m b e r o f p o s s i b l e e x c h a n g e = C_{2}^{5} = \frac{5 \times 4}{2 \times 1} = 10$

Case 2:

Number of electrons having same energy and spin (n) = 3

Minimum number of electrons required for exchange = 2

$\Rightarrow m a x i m u m n u m b e r o f p o s s i b l e e x c h a n g e = C_{r}^{n} = \frac{n!}{r! (n - r)!}$

$\Rightarrow m a x i m u m n u m b e r o f p o s s i b l e e x c h a n g e = C_{2}^{3} = \frac{3 \times 2}{2 \times 1} = 3$

Total number of possible exchange = 10 + 3 = 13

Q 3. Calculate the number of maximum possible exchanges in configuration d10?

Answer: (D)

Solution:

d10 configuration:

Case 1:

Number of electrons having same energy and spin (n) = 5

Minimum number of electrons required for exchange = 2

$\Rightarrow m a x i m u m n u m b e r o f p o s s i b l e e x c h a n g e = C_{r}^{n} = \frac{n!}{r! (n - r)!}$

$\Rightarrow m a x i m u m n u m b e r o f p o s s i b l e e x c h a n g e = C_{2}^{5} = \frac{5 \times 4}{2 \times 1} = 10$

Case 2:

Number of electrons having same energy and spin (n) = 5

Minimum number of electrons required for exchange = 2

$\Rightarrow m a x i m u m n u m b e r o f p o s s i b l e e x c h a n g e = C_{r}^{n} = \frac{n!}{r! (n - r)!}$

$\Rightarrow m a x i m u m n u m b e r o f p o s s i b l e e x c h a n g e = C_{2}^{5} = 10$

Total number of possible exchange = 10 + 10 = 20

Q 4. which configurations are most stable?

Answer: (D)

Solution: d10 is the most stable configuration because of its highest exchange energy and due to symmetricity.

Frequently asked questions-FAQs

Q. What is spin multiplicity?
Answer: Maximum spin multiplicity = 2|S|+1

|S| = Modulus of the maximum spin of an atom

Generally, the higher the spin multiplicity of any configuration more the stable configurations.

Q. Which Orbital has maximum symmetry?
Answer: ‘s’ orbitals are the most symmetrical orbitals because of their spherical shape.

Q. Is it necessary to start filling any orbitals with an upward arrow?
Answer: No, you can start filling orbitals with upward or downward spin but make sure, no electron pairing takes place in the orbitals in a sub-shell until each orbital is occupied by one electron with parallel spin.

Q. What are different subshells?
Answer: A group of orbitals building up the orbit/shell of an atom is called subshells. E.g- s subshell, p subshell, d subshell, f subshell