The total number of anti bonding molecular orbitals, formed from 2 s and 2 p atomic orbitals in a diatomic molecule is _______.

Solution

Chemistry ma’am · 3 steps

Orbitals in equals orbitals out: count the atomic orbitals, halve it, and you have the antibonding ones.

1. Count atomic orbitals. Each atom brings one 2s and three 2p orbitals, so 4 per atom. Two atoms give 4 + 4 = 8 atomic orbitals in total.
2. Conservation of orbitals. Combining atomic orbitals never creates or destroys any, so 8 atomic orbitals give 8 molecular orbitals. Each pair that combines gives one bonding and one antibonding MO, so 4 of the 8 are antibonding.

   Atomic orbitals combined	Bonding MO	Antibonding MO
   2s + 2s	σ 2s	σ^* 2s
   2p_z + 2p_z (end-on)	σ 2p_z	σ^* 2p_z
   2pₓ + 2pₓ (side-on)	π 2pₓ	π^* 2pₓ
   2p_y + 2p_y (side-on)	π 2p_y	π^* 2p_y

3. So. The antibonding orbitals are σ^* 2s, σ^* 2p_z, π^* 2pₓ and π^* 2p_y, giving 4.

The common slip: 3. Counting the degenerate π^* 2pₓ and π^* 2p_y as a single orbital gives 3, but they are two separate orbitals at the same energy.

The idea to keep. The number of MOs always equals the number of AOs that combine, and they split evenly into bonding and antibonding. Remember that π^* is a pair of degenerate orbitals, not one.

Answer from the NTA final answer key. Solution by PrepWiser.