When ψ_A and ψ_B are the wave functions of atomic orbitals, then σ^* is represented by :

Solution

Chemistry ma’am · 4 steps

Antibonding means the two waves cancel between the nuclei, so you subtract them, with equal weight.

1. LCAO idea. A molecular orbital is built by combining atomic orbitals: ψ_(MO) = ψ_A ± ψ_B. Adding gives one orbital, subtracting gives the other.
2. Bonding versus antibonding. Addition, ψ_A + ψ_B, makes the waves reinforce between the nuclei. That is the bonding orbital σ. Subtraction, ψ_A - ψ_B, makes them cancel, leaving a node between the nuclei. That is the antibonding orbital σ^*.

   σ^* = ψ_A - ψ_B

3. Equal weights. The two atoms in this combination contribute equally, so both coefficients have the same size. A factor of 2 on one orbital has no basis here, which rules out (a) and (c).
4. So. σ^* is represented by ψ_A - ψ_B, option (b).

The idea to keep. Plus sign means constructive overlap, so bonding. Minus sign means destructive overlap and a node between the nuclei, so antibonding. Keep the coefficients equal for identical atoms.

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