# Lecture 12: Aufbau Principle and Hund's Rule

Latest Version

Published a year ago

Latest Version

Published a year ago

#### Aufbau Principle - Building up of electrons

No more than 2 electrons can occupy an orbital or no 2 electrons in an atom can have all 4 quantum numbers the same. In other words- No 2 electrons in an atom can occupy all Y quantum # at the same time. Every electron in an atom has a unique set of the 4 quantum #. At least 1 quantum # should be different for 2 electrons.

#### Order of Increasing Energy (n+l)

$1S^{2},2S^{2},2P^{6},3S^{2},3P^{6},4S^{2},3d^{10},4P^{6}$

Electrons fill up orbitals by the increasing order of energy

### Hund's Rule of Maximum Multiplicity

- Electrons occupy degenerate orbitals singly if possible
- Electrons will occupy a set of degenerate orbitals with parallel spin as far as possible
- but other combinations are also possible but they are of higher energy of excited states

2P$^{3}$ Px Py Pz

$\uparrow$ $\uparrow$ $\uparrow$ $\rightarrow$ Obeying the Hund's Rule

$\uparrow$$\downarrow$ $\uparrow$ $\rightarrow$ Against Hund's Rule (Possible but for higher energy)

#### Extra Stability for Half-filled and Filled Shells.

- Be has a completely filled (S2) Configuration $\rightarrow$ stable $\rightarrow$ more energy is needed to remove an electron
- B has one electron in 2P $\rightarrow$ removed easily $\rightarrow$ low IE
- N has 2p$^{3}$ and is half-filled $\rightarrow$ stable $\rightarrow$ high IP
- O has 2p$^{4}$ and the 4$^{th}$ electron is in Px were there is already an electron $\rightarrow$ it is easy to remove $\rightarrow$ low IP

**Sum of power** - # Periodic Table

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