Aufbau Principle & Electronic Configuration

Aufbau Principle & $(n+l)$ Rule

Electronic Configuration | Structure of Atom | Class 11

1. What is the Aufbau Principle?

The word "Aufbau" is a German term that translates to "building up" or "construction". It is not the name of a scientist.

The Aufbau principle states that: "In the ground state of the atoms, the orbitals are filled with electrons in order of their increasing energies."

This means electrons first occupy the lowest energy orbital available before entering higher energy orbitals.

2. The $(n+l)$ Rule

The energy of an orbital is determined by the sum of its principal quantum number ($n$) and azimuthal quantum number ($l$). The filling sequence is strictly governed by the $(n+l)$ rule:

Rule 1: Orbitals with a lower value of $(n+l)$ have lower energy and are filled first.

Rule 2: If two orbitals have the same $(n+l)$ value, the orbital with the lower value of $n$ has lower energy and is filled first.

Example of the Rule

Compare $4s$ and $3d$ orbitals:

• For $4s$: $n=4$, $l=0 \implies (n+l) = 4 + 0 = 4$
• For $3d$: $n=3$, $l=2 \implies (n+l) = 3 + 2 = 5$

Since $4s$ has a lower $(n+l)$ value than $3d$, the $4s$ orbital is filled before $3d$.

3. Order of Filling Orbitals

Following the $(n+l)$ rule, the sequence in which the subshells are filled is:

$1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f < 5d < 6p < 7s ...$

4. Exceptional Configurations (Cr and Cu)

In a few cases, the actual electronic configuration slightly deviates from the strict Aufbau filling order. This occurs because half-filled and fully-filled subshells offer extra stability due to symmetry and higher exchange energy.

Chromium ($Cr$, $Z=24$)

• Expected: $[Ar] \ 4s^2 \ 3d^4$
• Actual: $[Ar] \ 4s^1 \ 3d^5$
• Reason: Shifting one electron from $4s$ to $3d$ gives a perfectly half-filled $3d^5$ subshell, which is highly stable.

Copper ($Cu$, $Z=29$)

• Expected: $[Ar] \ 4s^2 \ 3d^9$
• Actual: $[Ar] \ 4s^1 \ 3d^{10}$
• Reason: Shifting one electron from $4s$ to $3d$ gives a fully-filled $3d^{10}$ subshell, offering maximum stability.

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