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Chapter 26: Problem 6

Discuss Hund's rules for the determination of ground-state spectroscopic energy terms.

Short Answer

Expert verified
Hund's rules predict the ground-state term symbol and energy of an atom based on the multiplicity, the total orbital angular momentum (L), and total spin angular momentum (J). Rule 1 focuses on maximum multiplicity; Rule 2 looks at maximum L for given multiplicity; Rule 3 considers if the shell is less than half full or more than half full to determine which J is preferred.

Step by step solution

01

Understanding Hund’s Rules

Hund’s rules help us to determine the quantum state of an atom. The first rule states that the configuration with the highest multiplicity has the lowest energy. The multiplicity is determined by the number of unpaired electrons. The second rule stipulates that for a given multiplicity, the electronic configuration with the highest total orbital angular momentum quantum number L has the lowest energy. The last rule postulates that for a given multiplicity and a given L, the level with the largest total angular momentum quantum number J has the lowest energy if the electron shell is less than half full, whereas for more than half full shell, the level with smallest J has the lowest energy.
02

Apply Hund’s Rules - Rule 1

The maximum multiplicity results in a state where spins of electrons are unpaired and parallel, meaning they all spin in the same direction (either up or down). Number of unpaired electrons represents the multiplicity, therefore an atom with maximum unpaired electrons has minimum energy.
03

Apply Hund’s Rules - Rule 2

For configurations with the same multiplicity (equal number of unpaired electrons), the one with maximum total orbital angular momentum L having the lowest energy is preferred. The magnitude of L can increase if the unpaired electrons are as far apart as possible which minimizes the repulsive force between them.
04

Apply Hund’s Rules - Rule 3

For shells with the same L and multiplicity, the ground state term symbol is determined by whether the shell is less than half full or more than half full. If it is less than half full, the shell with the maximum total J is preferred, whereas for a more than half full shell, the shell with the minimum J is preferred.

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