Step 1: Understanding the Concept:
Molecular Orbital Theory (MOT) dictates that electrons fill bonding and antibonding orbitals based on energy. Antibonding orbitals are marked with a star (\(\sigma^*\) or \(\pi^*\)). Step 2: Key Formula or Approach:
Write the electronic configuration for each molecule and count electrons in starred (\(*\)) orbitals. Step 3: Detailed Explanation:
(A) \(\text{Li}_2\) (6 electrons): \(\sigma_{1s}^2 \sigma_{1s}^{*2} \sigma_{2s}^2\). Total antibonding electrons = 2.
(B) \(\text{N}_2\) (14 electrons): \(\sigma_{1s}^2 \sigma_{1s}^{*2} \sigma_{2s}^2 \sigma_{2s}^{*2} \pi_{2p_x}^2 \pi_{2p_y}^2 \sigma_{2p_z}^2\). Total antibonding electrons = 4.
(C) \(\text{O}_2\) (16 electrons): \(\dots \sigma_{2p_z}^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \pi_{2p_x}^{*1} \pi_{2p_y}^{*1}\). Total antibonding electrons = \(4 + 2 = 6\).
(D) \(\text{F}_2\) (18 electrons): \(\dots \sigma_{2p_z}^2 \pi_{2p_x}^2 \pi_{2p_y}^2 \pi_{2p_x}^{*2} \pi_{2p_y}^{*2}\). Total antibonding electrons = \(4 + 4 = 8\). Step 4: Final Answer:
\(\text{F}_2\) has the maximum number of antibonding electrons (8).