What are the steps outlined by Hund's rule to assign energies?

Hund's rule is essential in determining the ground state configuration of electrons in multi-electron atoms. It states that electrons will fill degenerate orbitals (orbitals of the same energy) singly before pairing up. The justification for the chosen answer is that it captures the essence of identifying the most stable configuration of electrons based on their spin and the distribution of their angular momentum across different orbitals.

The first step involves identifying the microstate with the highest spin multiplicity (MS), which reflects how many unpaired electrons can result from the arrangement. This is significant because a higher multiplicity corresponds to a more stable electron configuration due to reduced electron-electron repulsion. Following this, the next step is to identify the highest permitted magnetic quantum number (ML) for that multiplicity, ensuring that the configuration adheres to the rules governing orbital occupancy. In essence, this approach systematically maximizes the number of unpaired electrons while keeping them in the highest available energy levels.

This process not only aligns with Hund's rule but also provides a structured method to determine the relative energies of the orbitals, significantly contributing to understanding the electron structure in an atom. The rationale behind this sequence of steps leads to the most stable electronic arrangement, which is crucial for predicting chemical behavior