Which of the following correctly describes the molecular orbital energy diagram for the diatomic molecule Be_2?

• A. The diagram shows unpaired electrons in the antibonding orbitals, making Be_2 paramagnetic.
• B. The diagram shows filled bonding and antibonding orbitals, resulting in a bond order of 0.
• C. The diagram shows a bond order of 1, indicating a stable Be_2 molecule.
• D. The diagram shows only filled bonding orbitals, resulting in a bond order of 2.

Answer: (B)

Verified step by step guidance

1. Recall that the molecular orbital (MO) theory combines atomic orbitals to form molecular orbitals, which can be bonding or antibonding. Electrons fill these orbitals starting from the lowest energy level.
2. Determine the total number of valence electrons in Be_2. Each beryllium atom has 2 valence electrons, so Be_2 has a total of 4 valence electrons.
3. Fill the molecular orbitals with these 4 electrons according to the energy order for second period diatomic molecules. For Be_2, the order is typically: \(\sigma_{2s}\) (bonding), then \(\sigma^*_{2s}\) (antibonding).
4. Calculate the bond order using the formula: \(\text{Bond order} = \frac{(\text{number of electrons in bonding MOs}) - (\text{number of electrons in antibonding MOs})}{2}\). For Be_2, count how many electrons occupy bonding and antibonding orbitals.
5. Analyze the bond order result: if it is zero, the molecule is not stable and does not form a bond; if it is greater than zero, the molecule is stable. Also, check if there are unpaired electrons to determine if the molecule is paramagnetic or diamagnetic.