According to molecular orbital theory, how many bonding and antibonding molecular orbitals are formed from the combination of the valence atomic orbitals in methane (CH_4)?

• A. 2 bonding and 2 antibonding molecular orbitals
• B. 4 bonding and 4 antibonding molecular orbitals
• C. 6 bonding and 6 antibonding molecular orbitals
• D. 8 bonding and 8 antibonding molecular orbitals

Answer: (B)

Verified step by step guidance

1. Identify the valence atomic orbitals involved in bonding for methane (CH_4). Carbon has 4 valence orbitals (one 2s and three 2p orbitals), and each hydrogen has one 1s orbital. Since there are 4 hydrogens, there are 4 hydrogen 1s orbitals.
2. Combine the atomic orbitals from the hydrogens to form symmetry-adapted linear combinations (SALCs) that match the symmetry of the carbon valence orbitals. This results in 4 group orbitals from the hydrogens that can interact with the 4 carbon valence orbitals.
3. According to molecular orbital theory, when atomic orbitals combine, each pair of interacting orbitals forms one bonding molecular orbital and one antibonding molecular orbital.
4. Since there are 4 pairs of orbitals combining (4 carbon orbitals and 4 hydrogen SALCs), the total number of molecular orbitals formed is 8, consisting of 4 bonding and 4 antibonding molecular orbitals.
5. Therefore, the number of bonding and antibonding molecular orbitals formed from the valence atomic orbitals in methane is 4 bonding and 4 antibonding molecular orbitals.