To solve this problem, let's consider the principles mentioned:
Hund's Rule: It states that electrons will fill degenerate orbitals (orbitals with the same energy) singly before pairing. This means that every orbital in a subshell gets one electron each before any gets a second one, and all the single electrons have the same spin.
Pauli Exclusion Principle: It states that no two electrons in an atom can have the same set of all four quantum numbers. This implies that an orbital can hold a maximum of two electrons, and they must have opposite spins.
Let's analyze the given electron configurations based on these principles:
Configuration I: Shows one filled orbital with two electrons having opposite spins and one unfilled orbital. This satisfies both Hund's Rule and the Pauli Exclusion Principle.
Configuration II: Shows two filled orbitals, both with paired electrons having opposite spins. While it satisfies the Pauli Exclusion Principle, it doesn't follow Hund's Rule as an unpaired arrangement is energetically favorable unless necessary.
Configuration III: Shows two unpaired electrons in separate orbitals, each with the same spin. This follows Hund's Rule and doesn't violate the Pauli Exclusion Principle.
Configuration IV: Shows one orbital with paired electrons and one singly occupied orbital, following both Hund's Rule (the unpaired electrons are filled first) and Pauli Exclusion Principle.
Based on the analysis, the correct configurations are III and IV, as they satisfy both Hund's Rule and the Pauli Exclusion Principle.
Therefore, the correct answer is: Both III and IV.
