(a) How many valence electron are in B2+? (b) How many valence electrons of B2+ are in bonding molecular orbitals? (c) How many valence electrons of B2+ are in anti-bonding molecular orbitals? (d) What is the bond order of B2+? (e) If B2+ is a stable chemical species, what is it’s magnetism? (f) What type of molecular orbital contains the valence electron with the highest energy in B2+?
The Correct Answer and Explanation is:
⚛ Molecular Orbital Diagram for B₂⁺
For elements with atomic number ≤ 7 (like boron), the MO diagram is:
scssCopyEdit σ*(2p)
π*(2p) π*(2p)
π(2p) π(2p)
σ(2p)
σ*(2s)
σ(2s)
(a) How many valence electrons are in B₂⁺?
B atom: 5 electrons → 2 B atoms = 10 electrons
B₂⁺ loses 1 electron → 9 valence electrons
(b) How many valence electrons are in bonding molecular orbitals?
Bonding MOs: σ(2s), π(2p), σ(2p)
Filled as:
- σ(2s): 2 e⁻
- π(2p): 4 e⁻ (2 in each π orbital)
- σ(2p): 1 e⁻
→ 7 electrons in bonding orbitals
(c) How many valence electrons are in anti-bonding molecular orbitals?
Anti-bonding MOs: σ*(2s), π*(2p)
Filled as:
- σ*(2s): 2 e⁻
- π*(2p): 0 e⁻
→ 2 electrons in anti-bonding orbitals
(d) What is the bond order of B₂⁺?
Bond order = (Bonding e⁻ – Antibonding e⁻) ÷ 2
= (7 – 2) ÷ 2 = 2.5
(e) What is its magnetism?
Unpaired electrons = 1 (in σ(2p)) → Paramagnetic
(f) What type of MO contains the highest-energy valence electron?
Highest energy MO occupied = σ(2p)
📘 Explanation
The molecular orbital theory provides a more nuanced understanding of bonding in diatomic molecules by considering the combination of atomic orbitals to form molecular orbitals (MOs). In the case of B₂⁺ (a boron-boron cation), we begin by counting the total number of valence electrons. Each boron atom contributes 5 electrons, so neutral B₂ has 10. Since B₂⁺ has lost one electron, it contains 9 valence electrons.
The MO diagram for B₂⁺ follows the pattern used for lighter diatomic molecules (atomic numbers ≤ 7), where the energy ordering of the MOs is: σ(2s), σ*(2s), π(2p), σ(2p), π*(2p), σ*(2p). Electrons fill from the lowest energy levels upward according to the Aufbau principle, and obey Hund’s rule and the Pauli exclusion principle.
In B₂⁺, the electrons fill up to the σ(2p) orbital. We find two electrons in σ(2s), two in σ*(2s), four in the degenerate π(2p) orbitals, and one in the σ(2p). This results in 7 electrons in bonding MOs and 2 in anti-bonding MOs. The bond order, calculated as (bonding – anti-bonding)/2, gives 2.5, suggesting a fairly strong bond despite the loss of one electron.
Importantly, the presence of an unpaired electron in the σ(2p) orbital implies paramagnetism, meaning B₂⁺ is attracted to a magnetic field. This characteristic differentiates it from diamagnetic species, which have all electrons paired. Finally, the highest energy molecular orbital occupied in B₂⁺ is the σ(2p) orbital, which houses the unpaired electron and defines much of the ion’s chemical behavior.
This MO analysis helps predict not only bond strength but also magnetic properties, reactivity, and relative stability of molecules and ions like B₂⁺.
