Electron Configuration and Atomic Principles

The Three Fundamental Principles

1. The Aufbau Principle

The term "Aufbau" is German for "building up." This principle dictates that electrons occupy the available subshell of the lowest energy first. Once a subshell is filled, electrons move to the next higher energy level. The standard filling order is: $1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, \dots$

2. The Pauli Exclusion Principle

This rule asserts that no two electrons in a single atom can have the exact same set of four quantum numbers. In practical terms, this means an orbital can hold a maximum of two electrons, and they must have opposite spins. If you attempt to draw a configuration where two electrons in the same orbital have the same spin, the configuration is unacceptable.

3. Hund’s Rule

When filling degenerate orbitals (orbitals with the same energy, such as the three $p$ orbitals in a $2p$ subshell), electrons will occupy empty orbitals singly before they begin to pair up. Furthermore, these single electrons must all have parallel spins (usually represented as "spin up") to achieve the lowest energy state.

Exam Tip: Remember that orbitals are more stable when they are empty, half-filled, or completely filled. This is why elements like Chromium (Cr) and Copper (Cu) exhibit "exceptions" to the standard Aufbau order to achieve these more stable states.

Valence vs. Core Electrons

When looking at an atom's configuration, we distinguish between two types of electrons:

• Valence Electrons: The electrons located in the highest energy level. These are the electrons responsible for chemical bonding.
• Core Electrons: The inner electrons that occupy lower energy levels.

In the periodic table, the position of an element is directly related to its subshells. Representative elements are characterized by the filling of $ns$ subshells, while transition metals are characterized by the filling of $(n-1)d$ subshells.

Worked Example: Vanadium (V)

Let's apply these rules to Vanadium, which has 23 electrons.

1. Conventional (Longhand) Form: Following the Aufbau order: $1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^3$.

2. Shorthand Form: We use the nearest noble gas, which is Argon ([Ar]): $[Ar] 4s^2 3d^3$.

3. Determining Ion Configuration: When transition metals form cations, the electrons are removed from the highest energy level first. For Vanadium forming a $V^{+1}$ ion, we remove one electron from the $4s$ orbital: $V^{+1} = [Ar] 4s^1 3d^3$.

Magnetism and Unpaired Electrons

The presence of unpaired electrons significantly affects an atom's magnetic properties:

• Paramagnetic: Atoms with at least one unpaired electron are attracted to a magnetic field.
• Diamagnetic: Atoms with no unpaired electrons (all electrons are paired) are slightly repelled by a magnetic field.