Chapter 6, Problem 17CO

Interpretation Introduction

Interpretation: The electronic configurations for atoms and ions of main group elements are to be written using Pauli’s exclusion principle and Hund’s rule.

Concept introduction:

• Pauli Exclusion Principle states that no electrons can have same n, m, l and s values. Electrons having same n, m, l values belong to the same orbitals.
• Hund's rule states that every orbital in a subshell is singly occupied 1^st and after all the subshells are filled singly, the orbital is doubly occupied. All electrons are in same spin in singly occupied orbitals.

Answer to Problem 17CO

Solution: The electronic configuration of atoms and ions are written following the Pauli’s exclusion principle and Hund’s rule.

Mg: The electronic configuration is written as ${\text{1s}}^{\text{2}}{\text{2s}}^{\text{2}}{\text{2p}}^{\text{6}}{\text{3s}}^{\text{2}}$ or $\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }$

Mg²⁺: The electronic configuration is written as ${\text{1s}}^{\text{2}}{\text{2s}}^{\text{2}}{\text{2p}}^{\text{6}}{\text{3s}}^0$ or $\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{}$

C: The electronic configuration is written as ${\text{1s}}^{\text{2}}{\text{2s}}^{\text{2}}{\text{2p}}^4$ or $\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow }\boxed{\uparrow }$

F: The electronic configuration is written as ${\text{1s}}^{\text{2}}{\text{2s}}^{\text{2}}{\text{2p}}^5$ or $\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow }$

Explanation of Solution

Pauli’s exclusion principle and Hund’s rule are useful in writing electronic configurations of atoms and ions of main group elements.

Pauli Exclusion Principle states that no electrons can have same n, m, l and s values. The following table will be helpful in calculating the maximum number of electrons that can occupy a given shell.

Shell	n	l (n-1)	ml	ms	Electrons present	Total number of electrons
K	1	0	0	+1/2, -1/2	2	2
L	2	0 1	0 -1 0 1	+1/2, -1/2 +1/2, -1/2 +1/2, -1/2 +1/2, -1/2	2 2 2 2	8

For example, for 1s, 2s orbitals, the correct electronic configuration is $\underset{\_}{\uparrow \downarrow }\underset{\_}{\uparrow \downarrow }$ and not $\underset{\_}{\uparrow \downarrow }\underset{\_}{\uparrow \uparrow }$

Hund's rule states that every orbital in a subshell is singly occupied 1^st and after all the subshells are filled singly, the orbital is doubly occupied. All electrons are in same spin in singly occupied orbitals. For example, for 2p orbital, the correct electronic configuration is $\boxed{\uparrow }\boxed{\uparrow }\boxed{\uparrow }$ and not $\boxed{\uparrow \downarrow }\boxed{\uparrow }\boxed{}$ or $\boxed{\uparrow }\boxed{\downarrow }\boxed{\uparrow }$.

Using the Pauli’s exclusion principle and Hund’s rule, let us write the electronic configurations of some main group elements.

Mg: The electronic configuration is written as ${\text{1s}}^{\text{2}}{\text{2s}}^{\text{2}}{\text{2p}}^{\text{6}}{\text{3s}}^{\text{2}}$ or $\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }$

Mg²⁺: The electronic configuration is written as ${\text{1s}}^{\text{2}}{\text{2s}}^{\text{2}}{\text{2p}}^{\text{6}}{\text{3s}}^0$ or $\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{}$

C: The electronic configuration is written as ${\text{1s}}^{\text{2}}{\text{2s}}^{\text{2}}{\text{2p}}^4$ or $\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow }\boxed{\uparrow }$

F: The electronic configuration is written as ${\text{1s}}^{\text{2}}{\text{2s}}^{\text{2}}{\text{2p}}^5$ or $\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow }$

Conclusion

The electronic configuration of atoms and ions are written following the Pauli’s exclusion principle and Hund’s rule as follows:

Mg: The electronic configuration is written as ${\text{1s}}^{\text{2}}{\text{2s}}^{\text{2}}{\text{2p}}^{\text{6}}{\text{3s}}^{\text{2}}$ or $\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }$

Mg²⁺: The electronic configuration is written as ${\text{1s}}^{\text{2}}{\text{2s}}^{\text{2}}{\text{2p}}^{\text{6}}{\text{3s}}^0$ or $\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{}$

C: The electronic configuration is written as ${\text{1s}}^{\text{2}}{\text{2s}}^{\text{2}}{\text{2p}}^4$ or $\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow }\boxed{\uparrow }$

F: The electronic configuration is written as ${\text{1s}}^{\text{2}}{\text{2s}}^{\text{2}}{\text{2p}}^5$ or $\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow \downarrow }\boxed{\uparrow }$