Draw molecular orbital diagram for ${{F}_{2}}$ molecule. Also, gives its electronic configuration, bond order and magnetic property.

To understand the molecular orbital (MO) diagram for the fluorine molecule (F₂), we first need to consider the electronic configuration of the fluorine atom and how these configurations combine when two fluorine atoms bond together. Let's break this down step by step.

Electronic Configuration of Fluorine

The atomic number of fluorine is 9, which means each fluorine atom has 9 electrons. The electronic configuration for a single fluorine atom is:

• 1s² 2s² 2p⁵

This indicates that fluorine has two electrons in the 1s orbital, two in the 2s orbital, and five in the 2p orbitals. When two fluorine atoms come together to form F₂, we need to consider how these atomic orbitals will combine.

Molecular Orbital Diagram for F₂

In the molecular orbital theory, atomic orbitals combine to form molecular orbitals that can be occupied by the electrons of the molecule. For diatomic molecules like F₂, the relevant orbitals are the 1s, 2s, and 2p orbitals. The MO diagram for F₂ can be illustrated as follows:

1. Energy Levels and Orbital Mixing

In F₂, the 1s and 2s orbitals will form bonding and antibonding molecular orbitals:

• σ(1s) - bonding molecular orbital
• σ*(1s) - antibonding molecular orbital
• σ(2s) - bonding molecular orbital
• σ*(2s) - antibonding molecular orbital

For the 2p orbitals, the arrangement is slightly different due to the energy levels:

• σ(2p) - bonding molecular orbital
• π(2p) - degenerate bonding molecular orbitals
• π*(2p) - degenerate antibonding molecular orbitals
• σ*(2p) - antibonding molecular orbital

2. Filling the Molecular Orbitals

Now, we fill the molecular orbitals with the total number of electrons from both fluorine atoms. Since each fluorine contributes 9 electrons, F₂ has a total of 18 electrons:

• σ(1s) - 2 electrons
• σ*(1s) - 0 electrons
• σ(2s) - 2 electrons
• σ*(2s) - 0 electrons
• σ(2p) - 2 electrons
• π(2p) - 4 electrons (2 in each degenerate orbital)
• π*(2p) - 0 electrons
• σ*(2p) - 0 electrons

Electronic Configuration of F₂

The electronic configuration of the F₂ molecule in terms of molecular orbitals can be expressed as:

• (σ(1s))² (σ*(1s))⁰ (σ(2s))² (σ*(2s))⁰ (σ(2p))² (π(2p))⁴ (π*(2p))⁰ (σ*(2p))⁰

Bond Order Calculation

Bond order is calculated using the formula:

Bond Order = (Number of bonding electrons - Number of antibonding electrons) / 2

In F₂:

• Bonding electrons = 2 (σ(1s)) + 2 (σ(2s)) + 2 (σ(2p)) + 4 (π(2p)) = 10
• Antibonding electrons = 0 (σ*(1s)) + 0 (σ*(2s)) + 0 (π*(2p)) + 0 (σ*(2p)) = 0

Thus, the bond order is:

Bond Order = (10 - 0) / 2 = 5

Magnetic Properties of F₂

To determine the magnetic properties, we look at the presence of unpaired electrons. In the case of F₂, all electrons are paired in the molecular orbitals:

• σ(1s) - 2 paired
• σ(2s) - 2 paired
• σ(2p) - 2 paired
• π(2p) - 4 paired

Since there are no unpaired electrons, F₂ is classified as a diamagnetic molecule, meaning it is not attracted to a magnetic field.

Summary

In summary, the molecular orbital diagram for F₂ shows a total of 18 electrons, with a bond order of 1, indicating a single bond between the two fluorine atoms. Additionally, F₂ is diamagnetic due to the absence of unpaired electrons. This understanding of molecular orbitals helps explain the stability and properties of the F₂ molecule in a clear and structured manner.