What is the expected bond order for the diatomic species B_2?

• A. 1
• B. 2
• C. 0.5
• D. 3

Answer: (B)

Verified step by step guidance

1. Recall that bond order is calculated using the formula: \(\text{Bond order} = \frac{\text{Number of bonding electrons} - \text{Number of antibonding electrons}}{2}\).
2. Determine the total number of valence electrons in the B\(_2\) molecule. Since each boron atom has 3 valence electrons, B\(_2\) has \$3 \times 2 = 6$ valence electrons.
3. Fill the molecular orbitals with these 6 electrons according to the molecular orbital (MO) theory for diatomic molecules. For B\(_2\), the order of orbitals (from lowest to highest energy) is: \(\sigma_{2s}\), \(\sigma^*_{2s}\), \(\pi_{2p_x} = \pi_{2p_y}\), \(\sigma_{2p_z}\).
4. Place the 6 electrons into the MOs: 2 electrons fill \(\sigma_{2s}\), 2 electrons fill \(\sigma^*_{2s}\), and the remaining 2 electrons go into the degenerate \(\pi_{2p_x}\) and \(\pi_{2p_y}\) orbitals (one electron in each, following Hund's rule).
5. Count the bonding electrons (those in bonding orbitals) and antibonding electrons (those in antibonding orbitals), then apply the bond order formula to find the expected bond order for B\(_2\).