Quantum Numbers

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Which subshell is filled first according to the Aufbau principle?

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1. **Aufbau (n+l) Rule**: Orbitals are filled in order of increasing $(n+l)$ value.
2. **Comparison Table**:
   - $3p$: $n=3, l=1 \implies n+l = 4$
   - $4s$: $n=4, l=0 \implies n+l = 4$
   - $3d$: $n=3, l=2 \implies n+l = 5$
   - $4p$: $n=4, l=1 \implies n+l = 5$
3. **Tie-breaking Rule**: For equal $(n+l)$, the orbital with the **lower $n$** fills first.
4. **Analysis**: $3p$ (n=3) fills before $4s$ (n=4). Since $4s$ has $n+l=4$ and $3d$ has $n+l=5$, **$4s$ fills before $3d$**.
5. **Note**: This is why Potassium ($Z=19$) starts the 4th period before scandium starts the d-block.

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