# Lecture 12: Aufbau Principle and Hund's Rule

#### 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