Hund's Rule and Pauli's Exclusion Principle

Hund’s rule states that when filling sub-levels other than s orbital, electrons must not be spin paired in the orbitals until each orbital contains one electron, and no orbital can have two electrons with the same spin.

Pauli's Exclusion Principle states that no two electrons can have the same quantum numbers. An orbital can only hold 0, 1, or 2 electrons. They must have opposite spins if there are 2 electrons in the orbital.

When diagramming electrons filling sub-orbitals in each energy level and orbital, electrons are drawn as arrows to show the direction or spin that they are traveling. Recall from Hund's rule that electrons cannot be paired until each sub-orbital has one electron and that Pauli's exclusion principle states that each electron in every sub-orbital must spin in a different direction. Therefore, in each sub-orbital that holds two electrons, the first must spin upward, and the other must spin downward (see the image below; each line represents a sub-orbital).

An s-orbital has only one sub-orbital; p-orbitals have three sub-orbitals; d-orbitals have five sub-orbitals; and f-orbitals have seven sub-orbitals. Each sub-orbital can hold up to two electrons, spinning in opposite directions.

Orbitals and the Periodic Trend

Valence electron shells in the periodic table follow a trend. This can be referred to as the s block, the p block, the d block, and the f block (lanthanides and actinides), meaning that, in its ground state (lowest energy level), an element in a certain "block" will have its valence electrons in the s, p, d, or f orbitals depending on how many electrons it has.

How to Write Ground State Electron Configurations

The Basics

Electron configurations are written using the principal quantum number n, followed by the orbital (s, p, d, or f) with the total number of electrons written as superscripts. Example: 1s², a few main steps should be followed for writing ground state electron configurations.

1. Find the number of electrons in the atom. Example: Na: 11 e^- Na⁺: 10 e^-

2. Fill orbitals following the model until all electrons have been accounted for.

3. After that, it is important to check for a nearly half-filled or filled d orbital (d⁴ or d⁹) and adjust accordingly by removing an electron from the s orbital beneath it.

Example 1: Sodium (Na): 11 e^-

1s² 2s² 2p⁶ 3s¹

or

Na+: 1s² 2s² 2p⁶ (from the loss of 1 e^-)

Example 2: Chromium (Cr): 24

Cr: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁴ half-filled orbital, s orbital beneath it.

1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹ 3d⁵

The second line in the example is the actual electron configuration of chromium. It differs because the 4s orbital is beneath the 3d in energy. According to the filling order, chromium will fill the 3d orbital first with 5 electrons before adding the sixth electron to the 4s orbital, giving it a stable noble gas configuration. This results in greater stability for the chromium atom since the electrons are spaced out equally - each 3d sub-orbital is half-full, and the 4s orbital is half-full.

Shorthand Notation

Because writing the entire electron configuration can become cumbersome, there is a shorthand option. It uses the symbol of the noble gas (elements to the farthest right period) in the period above the element to represent the electron configuration before it.

Example:

Na: 1s² 2s² 2p⁶ 3s¹ is shortened to: [Ne] 3s¹.