Electronic Configuration Rules
Aufbau Principle, Hund's Rule & Pauli Exclusion Principle
1. Aufbau Principle (Building Up)
The (n + l) Rule
The energy of an orbital is determined by the sum of principal ($n$) and azimuthal ($l$) quantum numbers.
- Lower $(n+l)$ $\rightarrow$ Lower Energy.
- If $(n+l)$ is same for two orbitals, the one with lower $n$ has lower energy.
Order: $1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d \dots$
Example: $4s$ ($4+0=4$) fills before $3d$ ($3+2=5$).
2. Pauli Exclusion Principle
Consequence: An orbital can accommodate a maximum of 2 electrons, and they must have opposite spins ($\uparrow$ and $\downarrow$).
- Valid: ↑↓
- Invalid: ↑↑ or ↓↓
3. Hund's Rule of Maximum Multiplicity
Furthermore, singly occupied orbitals must have parallel spins to maximize stability (Exchange Energy).
Example (Nitrogen, $2p^3$): Correct: ↑↑↑
4. Exceptional Configurations
Half-filled and fully-filled orbitals are extra stable due to symmetry and higher exchange energy. This leads to deviations from the Aufbau principle.
Chromium (Z=24)
Expected: $[Ar] 4s^2 3d^4$
Actual: $[Ar] 4s^1 3d^5$ (Half-filled d-subshell)
Copper (Z=29)
Expected: $[Ar] 4s^2 3d^9$
Actual: $[Ar] 4s^1 3d^{10}$ (Fully-filled d-subshell)
5. Filling Capacities
| Subshell | Number of Orbitals | Max Electrons |
|---|---|---|
| s ($l=0$) | 1 | 2 |
| p ($l=1$) | 3 | 6 |
| d ($l=2$) | 5 | 10 |
| f ($l=3$) | 7 | 14 |
Practice Quiz
Test your knowledge on Electronic Configuration.
Nicely explained sir !
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