Question

What are Hund's Rule, Pauli Exclusion Principle, and Aufbau Principle? How are they different? How are they related?

Answer 1

• Aufbau Principle: lower energy orbitals fill before higher energy orbitals.
• Hund's Rule: one electron goes into each until all of them are half full before pairing up.
• Pauli Exclusion Principle: no two electrons can be identified by the same set of quantum numbers (i.e. must have
  different spins).

Explanation:

I'll start by explaining what each means, and then we'll talk about how they're related:

The Aufbau Principle states that lower energy orbitals fill before higher energy orbitals. For example, the orbitals in the `n=1` energy level will fill up before the orbitals in the `n=2` energy level.

Hund's Rule states that if 2 or more degenerate (i.e. same energy) orbitals are available, one electron goes into each until all of them are half full before pairing up . You may have heard this one in relation to the analogy of filling seats in a bus; everyone finds their own seat, and only when all the seats are half full do they start sitting together.

The Pauli Exclusion Principle states that no two electrons can be identified by the same set of quantum numbers. This is actually why we have the spin quantum number, `m_s`, to ensure that two electrons within the same orbital have unique sets of quantum numbers. You may also hear this in the form that the two electrons in an orbital must have opposite spins, which essentially means the same thing.

How are they related? Well, you might have already guessed, but put together they allow us to do a lot of work with electron configurations and energy diagrams. You may not see it directly, but as you work examples in these two topics, and start to think of why you're doing what you're doing, you'll see how these three principles are applied. You'll also see them again when you work with Molecular Orbital Theory.

Hope that helped :)