Answer
Determining Unpaired Electrons Using Hund’s Rule and Pauli Exclusion Principle
To determine the number of unpaired electrons in an atom, we must use two key quantum mechanical principles:
- Pauli Exclusion Principle: No two electrons in an atom can have the same set of quantum numbers. Each orbital can hold a maximum of two electrons with opposite spins.
- Hund’s Rule: Electrons fill degenerate orbitals (orbitals with the same energy) singly first, with parallel spins, to minimize electron repulsion.
1. Fluorine (Z = 9)
Electron Configuration: 1s² 2s² 2p⁵
The 2p orbital can hold 6 electrons. Here, it has 5 electrons.
According to Hund’s Rule, the first three 2p orbitals get one electron each, and the remaining two pair up.
➤ Unpaired Electrons: 1
2. Phosphorus (Z = 15)
Electron Configuration: 1s² 2s² 2p⁶ 3s² 3p³
The 3p subshell has 3 electrons. Each of the three 3p orbitals will contain one unpaired electron.
➤ Unpaired Electrons: 3
3. Titanium (Z = 22)
Electron Configuration: [Ar] 4s² 3d²
The 3d subshell can hold 10 electrons. Titanium has 2 electrons in the 3d subshell.
Each of these two 3d orbitals gets one electron (Hund’s Rule).
➤ Unpaired Electrons: 2
4. Cobalt (Z = 27)
Electron Configuration: [Ar] 4s² 3d⁷
The 3d subshell now contains 7 electrons.
Following Hund’s Rule, five 3d orbitals get one electron each first (5), then two of them pair up (2).
So, 3 unpaired electrons remain.
➤ Unpaired Electrons: 3