According to molecular orbital theory, would Be2 be expected to exist? Explain. Would Be2+ be expected to exist? Explain. What are the relationships among bond order, bond length, and bond energy?

Verified step by step guidance

1. Step 1: Begin by understanding the molecular orbital (MO) theory, which describes the distribution of electrons in molecules in terms of molecular orbitals that can extend over the entire molecule.
2. Step 2: Construct the molecular orbital diagram for Be2. Beryllium (Be) has an atomic number of 4, so each Be atom has 4 electrons. In Be2, there are a total of 8 electrons to place in molecular orbitals.
3. Step 3: Fill the molecular orbitals for Be2 starting from the lowest energy level. The order is: \( \sigma_{1s} \), \( \sigma_{1s}^* \), \( \sigma_{2s} \), \( \sigma_{2s}^* \). Place the 8 electrons accordingly.
4. Step 4: Calculate the bond order for Be2 using the formula: \( \text{Bond Order} = \frac{(\text{Number of electrons in bonding MOs} - \text{Number of electrons in antibonding MOs})}{2} \). Determine if the bond order is greater than zero to predict the existence of Be2.
5. Step 5: For Be2+, remove one electron from the highest occupied molecular orbital (HOMO) of Be2 and recalculate the bond order. Discuss the relationships among bond order, bond length, and bond energy: higher bond order generally means shorter bond length and higher bond energy.