What is the Pauli Aufbau rule?

The term "Pauli Aufbau rule" isn't a standard, recognized term in chemistry or physics. It seems to be a combination of two important principles governing electron configuration: the Aufbau principle and the Pauli Exclusion Principle. Therefore, a better question is: What are the Aufbau principle and the Pauli Exclusion Principle, and how do they work together to determine electron configurations?

Here's a breakdown of each principle:

The Aufbau Principle

The Aufbau principle, derived from the German word "Aufbau" meaning "building up," dictates the order in which electrons fill atomic orbitals.

• Core Concept: Electrons first occupy the lowest energy orbitals available before filling higher-energy orbitals.
• Analogy: Imagine filling a house with people. You'd fill the ground floor before moving to the second floor.
• Energy Levels: The filling order is generally: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p. This order can be predicted using the (n+l) rule, where 'n' is the principal quantum number and 'l' is the azimuthal quantum number. Lower (n+l) values indicate lower energy. If two orbitals have the same (n+l) value, the orbital with the lower 'n' value is filled first.
• Reference: According to the Aufbau Principle, "electrons will occupy lower-energy orbitals before moving on to higher-energy orbitals".

The Pauli Exclusion Principle

The Pauli Exclusion Principle, named after physicist Wolfgang Pauli, limits the number of electrons that can occupy a single atomic orbital.

• Core Concept: An atomic orbital can hold a maximum of two electrons, and these electrons must have opposite spins (spin-up and spin-down).
• Quantum Numbers: No two electrons in the same atom can have the same set of four quantum numbers (n, l, ml, ms). Since an orbital is defined by n, l, and ml, the only difference can be in the spin quantum number (ms), which can be either +1/2 or -1/2.
• Implication: This principle explains why atoms have distinct electron configurations and chemical properties.
• Reference: According to the Pauli Exclusion Principle, "an orbital can only hold a maximum of two electrons with opposing spins."

How They Work Together

These two principles are crucial for determining the electron configuration of an atom:

1. Aufbau Principle dictates which orbitals get filled first based on energy levels.
2. Pauli Exclusion Principle dictates how many electrons each orbital can hold (maximum of two with opposite spins).

Example:

Consider Carbon (atomic number 6).

1. Aufbau Principle: We start filling orbitals from the lowest energy level: 1s, then 2s, then 2p.
2. Pauli Exclusion Principle:
   • 1s orbital can hold a maximum of 2 electrons. We fill it: 1s²
   • 2s orbital can hold a maximum of 2 electrons. We fill it: 1s²2s²
   • 2p orbital can hold a maximum of 6 electrons. We have 2 electrons left (6 total - 2 in 1s - 2 in 2s = 2). So, we fill it partially: 1s²2s²2p²

Therefore, the electron configuration of carbon is 1s²2s²2p². Hund's Rule further refines how electrons fill degenerate orbitals (like the three 2p orbitals), stating that electrons will individually occupy each orbital before doubling up in any one orbital.