In terms of its electronic configuration and molecular orbital structure, is the B2+ molecular ion paramagnetic or diamagnetic?

Introduction / Context:
Paramagnetism and diamagnetism are important magnetic properties that depend on the presence or absence of unpaired electrons in atoms and molecules. This question asks specifically about the B2+ molecular ion, which is best analysed using molecular orbital theory. Understanding how to count electrons and place them into molecular orbitals is essential for predicting whether a molecule is paramagnetic or diamagnetic.

Given Data / Assumptions:

• Boron has atomic number 5 and therefore 5 electrons in a neutral atom.
• The B2 molecule would have 10 electrons in total.
• The B2+ ion has one electron fewer than B2, so it has 9 electrons in total.
• Magnetic behaviour depends on whether there are unpaired electrons in the molecular orbitals.

Concept / Approach:
In simple molecular orbital theory for homonuclear diatomic molecules of light atoms, the order of orbitals up to the 2p level is sigma 1s, sigma 1s star, sigma 2s, sigma 2s star, then pi 2p and sigma 2p. For the B2 molecule with 10 electrons, the electrons fill up to the pi 2p orbitals, and there are unpaired electrons in these degenerate pi orbitals, giving paramagnetic behaviour. For B2+, one electron is removed from the highest occupied molecular orbital. Because the number of electrons becomes odd, it is not possible for all of them to be paired. Therefore at least one electron remains unpaired, which results in paramagnetism. Diamagnetism would require that all electrons are paired, which is not the case here.

Step-by-Step Solution:
Step 1: Count the electrons in neutral B2: each B contributes 5, so B2 has 10 electrons.Step 2: Remove one electron to form B2+, leaving 9 electrons available for the molecular orbitals.Step 3: Recall the approximate filling order for light diatomic molecules: sigma 1s, sigma 1s star, sigma 2s, sigma 2s star, then pi 2p orbitals.Step 4: Fill these orbitals with 9 electrons following the Pauli principle and Hund rule; the last occupied orbital will contain an unpaired electron.Step 5: Note that an odd total number of electrons makes complete pairing impossible, guaranteeing at least one unpaired electron.Step 6: Conclude that B2+ has unpaired electrons and is therefore paramagnetic rather than diamagnetic.

Verification / Alternative check:
A simple rule of thumb is that species with an odd number of electrons cannot have all electrons paired, so they must be paramagnetic. Since B2+ has 9 electrons, this rule alone suggests paramagnetic behaviour. More detailed molecular orbital diagrams found in standard inorganic or physical chemistry texts confirm that the appropriate highest occupied orbital for B2 and B2+ contains unpaired electrons, leading to observable paramagnetism.

Why Other Options Are Wrong:
The option Diamagnetic would require all electrons to be paired, which is impossible with 9 electrons distributed in molecular orbitals. The idea that the magnetism depends only on temperature ignores the key role of electron pairing and molecular structure. The suggestion that it cannot be determined from molecular orbital theory is incorrect because molecular orbital analysis is precisely the standard method used to determine the magnetic character of diatomic molecules like B2+.

Common Pitfalls:
Students sometimes confuse the neutral B2 molecule with its ion and may incorrectly apply the electron count of 10 instead of 9. Others rely on memory of specific examples without understanding the underlying orbital filling principles. A simple precaution is to always count the total electrons carefully and to remember that any species with an odd number of electrons must be paramagnetic in basic molecular orbital theory.

Final Answer:
The B2+ molecular ion is paramagnetic because it has an unpaired electron.