The Aufbau Principle

The Diagonal Rule (Aufbau Diagram)

• To determine the filling order, one can list subshells in rows by principal quantum number and draw diagonal arrows from the top-right to the bottom-left.
• The sequence follows the path: $1s \rightarrow 2s \rightarrow 2p \rightarrow 3s \rightarrow 3p \rightarrow 4s \rightarrow 3d \rightarrow 4p$, and so on.

Writing Configurations

• Full Configuration: Lists every subshell and its electron count, such as $1s^2 2s^2 2p^6$ for Neon.
• Condensed (Noble Gas) Configuration: Simplifies the notation by using the symbol of the previous noble gas in brackets to represent the 'core' electrons, followed by the remaining 'valence' electrons (e.g., $[He] 2s^2 2p^6$ for Neon).

Orbital Diagrams

• These visual tools use boxes or lines to represent orbitals and arrows to represent electrons, showing both the energy level and the electron spin.

Understanding the difference between core and valence electrons is vital for predicting chemical behavior.

• Subshell vs. Orbital: A subshell (like $2p$) is a group of orbitals with the same energy, while an orbital is the specific region (like $2p_x$) that holds a maximum of two electrons.

• The 4s/3d Overlap: Always remember that the $4s$ subshell is lower in energy than the $3d$ subshell and must be filled first in the Aufbau sequence.

• Check the Total: When writing a configuration, sum the exponents to ensure they equal the atomic number of the neutral atom; this is a quick way to catch missing subshells.

• Noble Gas Selection: When using condensed notation, always use the noble gas from the row above the element in question, never the noble gas in the same row.

• Valence Identification: For main group elements, the number of valence electrons usually corresponds to the group number (1-8), which helps verify the end of your configuration.

• Numerical Filling Error: A common mistake is filling all $n=3$ orbitals ($3s, 3p, 3d$) before moving to $n=4$. The Aufbau Principle requires $4s$ to fill before $3d$ due to lower energy.

• Exponent Confusion: Students often confuse the maximum capacity of subshells. Remember: $s=2$, $p=6$, $d=10$, and $f=14$.

• Ignoring Neutrality: Ensure you are using the correct number of electrons for ions versus neutral atoms; positive ions have fewer electrons than the atomic number suggests.