The molecular orbitals formed from 2s and 2p atomic orbitals are as fo
The problem asks for the total number of molecular orbitals that are formed by the combination of the 2s and 2p atomic orbitals from the two atoms in a diatomic molecule.
Concept Used:
The formation of molecular orbitals (MOs) is explained by the Linear Combination of Atomic Orbitals (LCAO) theory. The fundamental principle of this theory is the conservation of orbitals, which states that the total number of molecular orbitals formed is always equal to the total number of atomic orbitals (AOs) that are combined.
\[
\text{Number of Molecular Orbitals formed} = \text{Number of Atomic Orbitals combined}
\]
Step-by-Step Solution:
Step 1: Identify the atomic orbitals contributed by the first atom.
For one atom, we are considering the atomic orbitals in the second principal energy level (n=2). These are:
One 2s orbital.
Three 2p orbitals (which are 2pₓ, 2pᵧ, and 2p₂).
So, the first atom contributes a total of \(1 + 3 = 4\) atomic orbitals.
Step 2: Identify the atomic orbitals contributed by the second atom.
Since the molecule is diatomic, there is a second atom. This second atom also contributes its 2s and 2p atomic orbitals for bonding.
One 2s orbital.
Three 2p orbitals (2pₓ, 2pᵧ, and 2p₂).
The second atom also contributes a total of \(1 + 3 = 4\) atomic orbitals.
Step 3: Calculate the total number of atomic orbitals being combined.
The total number of atomic orbitals from both atoms is the sum of the orbitals contributed by each atom.
\[
\text{Total AOs} = (\text{AOs from atom 1}) + (\text{AOs from atom 2})
\]
\[
\text{Total AOs} = 4 + 4 = 8
\]
So, a total of 8 atomic orbitals are combined.
Final Computation & Result:
Step 4: Apply the principle of conservation of orbitals to find the total number of molecular orbitals.
According to the LCAO theory, the number of molecular orbitals formed must be equal to the number of atomic orbitals that were combined.
\[
\text{Number of MOs} = \text{Total AOs} = 8
\]
These 8 molecular orbitals are typically designated as \( \sigma_{2s}, \sigma^*_{2s}, \sigma_{2p}, \pi_{2p_x}, \pi_{2p_y}, \pi^*_{2p_x}, \pi^*_{2p_y}, \sigma^*_{2p} \).
The total number of molecular orbitals formed is 8.
