Which of the following molecules is diamagnetic according to molecular orbital theory?

• A. B_2
• B. C_2
• C. N_2
• D. O_2

Answer: (B)

Verified step by step guidance

1. Recall that a molecule is diamagnetic if all its electrons are paired in molecular orbitals, and paramagnetic if it has one or more unpaired electrons.
2. Write the total number of valence electrons for each molecule: B_2 has 10 electrons, C_2 has 12 electrons, N_2 has 14 electrons, and O_2 has 16 electrons.
3. Use the molecular orbital (MO) energy diagram for homonuclear diatomic molecules from the second period to fill the electrons into the molecular orbitals in order of increasing energy. Note that for B_2, C_2, and N_2, the ordering of the \( \sigma_{2p} \) and \( \pi_{2p} \) orbitals differs from that of O_2.
4. Fill the electrons into the MOs according to the correct order: for B_2, C_2, and N_2, the order is \( \sigma_{2s} < \sigma_{2s}^* < \pi_{2p} < \sigma_{2p} < \pi_{2p}^* < \sigma_{2p}^* \), and for O_2, the order is \( \sigma_{2s} < \sigma_{2s}^* < \sigma_{2p} < \pi_{2p} < \pi_{2p}^* < \sigma_{2p}^* \).
5. Determine the electron pairing in each molecule's MO diagram: identify which molecules have all electrons paired (diamagnetic) and which have unpaired electrons (paramagnetic).