Question

The total number of molecular orbitals formed from 2s and 2p atomic orbitals of a diatomic molecule is _________.

Answer 1

Correct Answer: 8

The problem requires determining the total number of molecular orbitals generated from the combination of 2s and 2p atomic orbitals originating from two atoms within a diatomic molecule.

Concept Utilized:

The formation of molecular orbitals (MOs) is elucidated by the Linear Combination of Atomic Orbitals (LCAO) theory. This theory's core principle is orbital conservation: the total count of molecular orbitals formed invariably equals the total count of atomic orbitals (AOs) that undergo combination.

\[ \text{Number of Molecular Orbitals formed} = \text{Number of Atomic Orbitals combined} \]

Step-by-Step Solution:

Step 1: Identify the atomic orbitals contributed by the first atom.

For a single atom, we consider the atomic orbitals within the second principal energy level (n=2), which are:

• One 2s orbital.
• Three 2p orbitals (specifically, 2pₓ, 2pᵧ, and 2p₂).

Thus, the first atom contributes a total of \(1 + 3 = 4\) atomic orbitals.

Step 2: Identify the atomic orbitals contributed by the second atom.

As the molecule is diatomic, a second atom is present. This atom also contributes its 2s and 2p atomic orbitals for bonding purposes.

• One 2s orbital.
• Three 2p orbitals (2pₓ, 2pᵧ, and 2p₂).

The second atom likewise contributes a total of \(1 + 3 = 4\) atomic orbitals.

Step 3: Calculate the total number of atomic orbitals being combined.

The aggregate number of atomic orbitals from both atoms is the sum of the orbitals each atom contributes.

\[ \text{Total AOs} = (\text{AOs from atom 1}) + (\text{AOs from atom 2}) \] \[ \text{Total AOs} = 4 + 4 = 8 \]

Consequently, a total of 8 atomic orbitals are combined.

Final Computation & Result:

Step 4: Apply the principle of orbital conservation to ascertain the total number of molecular orbitals.

In accordance with LCAO theory, the number of molecular orbitals generated must equal the number of atomic orbitals that were combined.

\[ \text{Number of MOs} = \text{Total AOs} = 8 \]

These 8 molecular orbitals are conventionally denoted as \( \sigma_{2s}, \sigma^*_{2s}, \sigma_{2p}, \pi_{2p_x}, \pi_{2p_y}, \pi^*_{2p_x}, \pi^*_{2p_y}, \sigma^*_{2p} \).

The total count of molecular orbitals generated is 8.