To determine the bond order and magnetic nature of B₂ assuming Hund's rule is violated, we first need to understand the molecular orbital configuration of B₂.

Boron (B) has an atomic number of 5, so its electron configuration is $1s^{2}2s^{2}2p^1$. For the diatomic molecule B₂, there are a total of 10 electrons (5 from each boron atom).

The molecular orbital energy order for B₂ is:

$\sigma 1_s{}^{\ast }<\sigma 1_s<\sigma 2_s{}^{\ast }<\sigma 2_s<\pi {2p}_x=\pi {2p}_y<\sigma 2_{p}z<\pi {2p}_x^{\ast }=\pi {2p}_y^{\ast }<\sigma 2_p^z{}^{\ast }$

Step 1: Fill the molecular orbitals in order of increasing energy, ignoring Hund's rule (which normally maximizes unpaired electrons). Without Hund's rule, we pair electrons as early as possible.

For B₂ (10 electrons):

• $\sigma 1_s$: 2 electrons (paired)
• $\sigma 1_s{}^{\ast }$: 2 electrons (paired)
• $\sigma 2_s$: 2 electrons (paired)
• $\sigma 2_s{}^{\ast }$: 2 electrons (paired)
• Now, the next orbitals are degenerate: $\pi {2p}_x$ and $\pi {2p}_y$. With 2 electrons remaining, we place both in the same π orbital (say $\pi {2p}_x$), pairing them.

So, the molecular orbital configuration becomes: $\left(\sigma 1_s{}^2\right)\left(\sigma 1_s{}^{\ast }{}^2\right)\left(\sigma 2_s{}^2\right)\left(\sigma 2_s{}^{\ast }{}^2\right)\left(\pi {2p}_x{}^2\right)$

Step 2: Calculate bond order. Bond order = (Number of bonding electrons - Number of antibonding electrons)/2

Bonding orbitals: $\sigma 1_s$ (2), $\sigma 2_s$ (2), $\pi {2p}_x$ (2) → total bonding electrons = 6

Antibonding orbitals: $\sigma 1_s{}^{\ast }$ (2), $\sigma 2_s{}^{\ast }$ (2) → total antibonding electrons = 4

Bond order = (6 - 4)/2 = 1

Step 3: Determine magnetic nature. Since all electrons are paired (no unpaired electrons), the molecule is diamagnetic.

Final answer: Bond order is 1 and the molecule is diamagnetic.

Related Topics and Formulae

Molecular Orbital Theory (MOT): Explains bonding in molecules using molecular orbitals formed by the combination of atomic orbitals. Bond order indicates the strength and stability of the bond.

Bond Order Formula: Bond order = (Number of electrons in bonding orbitals - Number of electrons in antibonding orbitals) / 2

Magnetic Nature: Paramagnetic if there are unpaired electrons (attracted to magnetic field), diamagnetic if all electrons are paired (slightly repelled by magnetic field).

Hund's Rule: In ground state, electrons occupy degenerate orbitals singly before pairing. Violating it means pairing electrons prematurely.