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

Solution

Chemistry ma’am · 3 steps

Orbitals are never created or lost: count the atomic orbitals going in, and that many MOs come out.

1. Conservation rule. In MO theory, n atomic orbitals always combine to give exactly n molecular orbitals. Half are bonding and half are antibonding.
2. Count per atom. Each atom brings one 2s orbital and three 2p orbitals (2pₓ, 2p_y, 2p_z). That is 4 atomic orbitals per atom.

   Atomic orbitals combined	Number of AOs	Molecular orbitals formed
   2s + 2s	2	σ 2s, σ^* 2s
   2p_z + 2p_z	2	σ 2p_z, σ^* 2p_z
   2pₓ + 2pₓ and 2p_y + 2p_y	4	π 2pₓ, π 2p_y, π^* 2pₓ, π^* 2p_y
   Total	8	8 MOs (4 bonding, 4 antibonding)

3. So. Two atoms give 2 × 4 = 8 atomic orbitals, so the total number of molecular orbitals is 8.

The common slip: 4. Counting the orbitals of only one atom gives 4, not 8. Both atoms contribute their 2s and 2p orbitals.

The idea to keep. Number of MOs always equals the number of AOs that combine. Count the orbitals from both atoms, and every bonding MO has an antibonding partner.

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