Question

When writing the electron configuration notation for an atom, what three principles or rules should you follow?

Short answer

When writing the electron configuration notation for an atom, the three principles to follow are: $1)$ Aufbau Principle - electrons fill orbitals in increasing order of their energy levels; $2)$ Pauli Exclusion Principle - no two electrons can have the same set of quantum numbers, so each orbital can hold only two electrons with opposite spins; and $3)$ Hund's Rule - when there are multiple orbitals with the same energy level, electrons should fill these orbitals with the maximum number of electrons having the same spin, before pairing up with opposite spin electrons.

Step-by-step solution

1. Aufbau Principle

The Aufbau Principle states that electrons should be added to the lowest energy orbitals first, before filling the higher energy ones. In other words, electrons should fill the orbitals in increasing order of their energy levels.

2. Pauli Exclusion Principle

The Pauli Exclusion Principle states that no two electrons in an atom can have the same set of quantum numbers. Since there are four quantum numbers and the last one (spin) can have two values (spin-up, +1/2, or spin-down, -1/2), each orbital can hold only two electrons with opposite spins.

3. Hund's Rule

Hund's Rule states that when there are multiple orbitals with the same energy level (degenerate orbitals), electrons should fill these orbitals in such a way that the maximum number of electrons has the same spin. In practical terms, electrons should be distributed in the degenerate orbitals, one per orbital, before pairing up with the opposite spin electron in an orbital. When writing the electron configuration notation for an atom, one should follow these three principles to ensure an accurate representation of its electron arrangement.

Key concepts

Understanding the Aufbau Principle

The Aufbau Principle is fundamental in explaining how electrons occupy the orbitals of an atom. It outlines that electrons fill atomic orbitals in a specific order, prioritizing lower energy levels first before moving onto the higher ones.

Think of it as a hotel with many floors; guests (electrons) check-in starting at the lowest floor (lowest energy level) and gradually fill up the higher floors (higher energy levels) as the lower ones become fully occupied. The order in which the 'rooms' (orbitals) are filled is determined by the 'address' (quantum numbers) of each room.

This principle helps us predict the electron configuration of an atom, which is critical for understanding an element's reactivity, bonding behavior, and properties. Remember, the correct order follows the increasing energy of orbitals, which generally fills the 1s before 2s, then 2p, and so on.

Applying the Pauli Exclusion Principle

The Pauli Exclusion Principle is a rule that essentially says no two guests (electrons) can stay in the exact same room (orbital) under identical conditions. Every electron has a unique set of quantum numbers, like a special key to their room.

Each orbital, which we can imagine as a room with two beds, can hold a maximum of two electrons, and these two must have opposite spins — one spin-up $+1/2$ and one spin-down $-1/2$. Think of spin as the direction in which the guests are facing; one must face one way, and the other the opposite. This ensures that each electron has its own place, and the principles of physics are not violated within the atom. By following the Pauli Exclusion Principle, we avoid 'overcrowding' any orbital, maintaining the unique identity and behavior of elements.

Hund's Rule and Electron Arrangement

Hund's Rule deals with the arrangement of electrons across orbitals of the same energy, known as degenerate orbitals. Imagine a row of identical rooms on the same floor; according to Hund's Rule, each electron would prefer to have its own room before sharing.

Electrons are filled into these rooms one at a time with the same spin. Only after every room has one electron will they start pairing up. This is akin to a group of people (electrons) entering a theater (atom); they would typically spread out with one person per row (degenerate orbital) before sitting next to someone. This rule helps to minimize the electron repulsion within the atom and is essential for understanding why certain electron configurations are more stable than others.