Draw the molecular orbital diagram for B2

Draw the molecular orbital diagram for B2. The number of unpaired electrons in the B2 molecule is _.

A. zero

B. 1

C. 2

D. 3

E. 4

The correct answer and explanation is:

The correct answer is C. 2.

Explanation:

Boron (B) has an atomic number of 5, which means each boron atom has 5 electrons. For the B₂ molecule, there are 10 electrons in total. These electrons fill the molecular orbitals in the order of increasing energy, based on the molecular orbital theory.

Molecular Orbitals for Diatomic Molecules:

The molecular orbital diagram for a diatomic molecule like B₂ consists of bonding and antibonding orbitals formed by the atomic orbitals of each atom. The order of filling for molecular orbitals in the case of homonuclear diatomic molecules like B₂ depends on whether the molecule is in the first or second row of the periodic table.

For B₂, the relevant orbitals are:

• σ(1s), σ*(1s), σ(2s), σ*(2s), σ(2pz), π(2px) = π(2py), π*(2px) = π*(2py), and σ*(2pz).

Filling the Orbitals:

1. The lowest-energy molecular orbitals, σ(1s) and σ*(1s), each can hold two electrons. These orbitals are filled first.
2. Next, the σ(2s) and σ*(2s) orbitals are filled, with each orbital holding two electrons.
3. After the σ*(2s) orbital, the next molecular orbitals to be filled are the σ(2pz), followed by the degenerate π(2px) and π(2py) orbitals. Each of these orbitals can hold two electrons.

In the case of B₂, the total of 10 electrons fills the following orbitals:

• σ(1s) (2 electrons)
• σ*(1s) (2 electrons)
• σ(2s) (2 electrons)
• σ*(2s) (2 electrons)
• σ(2pz) (2 electrons)
• The remaining electrons fill the degenerate π(2px) and π(2py) orbitals. In total, B₂ has two unpaired electrons in these π orbitals.

Thus, B₂ has two unpaired electrons, leading to the correct answer C. 2. These unpaired electrons are responsible for the paramagnetic properties of the B₂ molecule.