The total number of anti bonding molecular orbitals, formed from 2s and 2p atomic orbitals in a diatomic molecule is _____________.
Correct Answer: 4
Approach Solution - 1
In a diatomic molecule, when combining atomic orbitals, both bonding and anti-bonding molecular orbitals are formed. For atomic orbitals 2s and 2p:
- Combination of 2s orbitals: When two 2s orbitals overlap, they form one bonding (σ2s) and one anti-bonding (σ2s*) molecular orbital.
- Combination of 2p orbitals: The 2p orbitals split into three types: σ and two π orbitals. This results in bonding and anti-bonding combinations:
- σ2p orbitals: Form one σ2p and one σ2p* orbital.
- π2p orbitals: Each set forms two degenerate π2p and π2p* orbitals. Since there are two sets, this results in two bonding π2p orbitals and two antibonding π2p* orbitals.
Total number of anti-bonding orbitals:
- From 2s: 1 σ2s* orbital.
- From 2p: 1 σ2p* and 2 π2p* orbitals.
Total anti-bonding orbitals = 1 (from 2s) + 1 (from σ2p*) + 2 (from 2 π2p*) = 4.
This total, 4, falls within the given range (4,4).
Approach Solution -2
In molecular orbital theory, the anti-bonding molecular orbitals formed from atomic orbitals are as follows:
- Anti-bonding molecular orbital from 2s: 1
- Anti-bonding molecular orbitals from 2p: 3
Thus, the total number of anti-bonding molecular orbitals is:
\(1 + 3 = 4\)
The Correct Answer is: 4
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