Explain the diamagnetic behaviour of `F_(2)` molecule on the basis of molecular orbital theory.

Answer

To explain the diamagnetic behavior of the F₂ molecule based on Molecular Orbital Theory (MOT), we can follow these steps:

### Step 1: Determine the Total Number of Electrons in F₂
The F₂ molecule consists of two fluorine atoms. Each fluorine atom has 9 electrons, so the total number of electrons in F₂ is:
\[ 9 + 9 = 18 \text{ electrons} \]

### Step 2: Understand the Molecular Orbital Energy Levels
In MOT, the molecular orbitals are formed by the combination of atomic orbitals. For F₂, the relevant atomic orbitals are the 1s, 2s, and 2p orbitals. The energy levels of these orbitals can be arranged as follows:
- The 1s orbitals combine to form a bonding (σ1s) and an antibonding (σ*1s) molecular orbital.
- The 2s orbitals combine to form a bonding (σ2s) and an antibonding (σ*2s) molecular orbital.
- The 2p orbitals combine to form bonding (σ2p) and antibonding (σ*2p) molecular orbitals, along with two degenerate π2p orbitals (π2p_x and π2p_y).

### Step 3: Fill the Molecular Orbitals with Electrons
We will fill the molecular orbitals according to the Aufbau principle, Hund's rule, and the Pauli exclusion principle. The filling order for F₂ is:
1. σ1s (2 electrons)
2. σ*1s (0 electrons)
3. σ2s (2 electrons)
4. σ*2s (0 electrons)
5. σ2p (2 electrons)
6. π2p_x (2 electrons)
7. π2p_y (2 electrons)
8. σ*2p (0 electrons)
9. π*2p_x (0 electrons)
10. π*2p_y (0 electrons)

Now, we fill the 18 electrons:
- σ1s: 2
- σ*1s: 0
- σ2s: 2
- σ*2s: 0
- σ2p: 2
- π2p_x: 2
- π2p_y: 2
- σ*2p: 0

This gives us a total of 16 electrons filled in the bonding orbitals.

### Step 4: Check for Unpaired Electrons
After filling all the molecular orbitals, we find that all the electrons in the bonding orbitals are paired. Specifically, the π2p_x and π2p_y orbitals each contain 2 electrons, meaning there are no unpaired electrons in the F₂ molecule.

### Step 5: Conclusion on Diamagnetic Behavior
Since there are no unpaired electrons in the F₂ molecule, it exhibits diamagnetic behavior. Diamagnetic substances are characterized by the absence of unpaired electrons, which means they do not have a net magnetic moment and are not attracted to a magnetic field.

### Summary
Thus, based on Molecular Orbital Theory, the F₂ molecule is diamagnetic because all 18 electrons are paired in the molecular orbitals.

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