Give the molecular orbital description of B2 molecule.
The Correct Answer and Explanation is:
The molecular orbital theory describes the bonding in molecules by considering the interaction between atomic orbitals of the atoms that make up the molecule. For the B2 molecule, which consists of two boron atoms, the molecular orbitals are formed by the combination of their atomic orbitals. Here’s the detailed molecular orbital description for B2:
Atomic Orbitals Involved
Boron (B) has an atomic number of 5, which means each boron atom has 5 electrons. The electrons occupy the 1s, 2s, and 2p orbitals. When two boron atoms bond to form B2, the atomic orbitals combine to form molecular orbitals.
Molecular Orbitals
The molecular orbitals of B2 can be categorized as bonding or antibonding:
- Sigma (σ) orbitals: These are formed by the head-on overlap of orbitals along the internuclear axis.
- The σ(2s) orbital is the bonding molecular orbital formed by the overlap of the 2s orbitals of both boron atoms.
- The σ(2s)* orbital is the antibonding counterpart formed by the out-of-phase overlap of the 2s orbitals.
- Pi (π) orbitals: These result from the sideways overlap of the p orbitals.
- The π(2p) bonding molecular orbitals are formed by the overlap of the 2p orbitals on the two boron atoms.
- The π(2p)* antibonding molecular orbitals are formed by the out-of-phase overlap of the 2p orbitals.
- Sigma (σ) (2p): This is a bonding molecular orbital formed by the head-on overlap of the 2p orbitals.
- *Sigma(2p)**: This is the antibonding orbital formed by the out-of-phase overlap of the 2p orbitals.
Electron Configuration
Boron (B) has 5 electrons, so for B2, we have a total of 10 electrons. The electron configuration of the B2 molecule in its ground state is:
- σ(2s)², σ(2s)², π(2p)², π(2p)²**
Here’s how the electrons fill the molecular orbitals:
- The bonding σ(2s) and π(2p) orbitals are filled first, as they are lower in energy.
- The antibonding σ(2s)* and π(2p)* orbitals are then filled, though they do not contribute to bonding.
Bond Order
The bond order can be calculated as:Bond Order=12[(number of electrons in bonding orbitals)−(number of electrons in antibonding orbitals)]\text{Bond Order} = \frac{1}{2} [\text{(number of electrons in bonding orbitals)} – \text{(number of electrons in antibonding orbitals)}]Bond Order=21[(number of electrons in bonding orbitals)−(number of electrons in antibonding orbitals)]
For B2:
- Bonding electrons = 2 (σ(2s)) + 2 (π(2p)) = 4
- Antibonding electrons = 2 (σ*(2s)) + 2 (π*(2p)) = 4
Bond order = 1/2 * (4 – 4) = 0.
This bond order suggests that the B2 molecule is very weakly bonded or may not exist under normal conditions. This result is consistent with the fact that B2 is generally unstable in isolation and requires specific conditions to exist.
