Using the molecular orbital theory, predict how many unpaired electrons are in the B22– ion.

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Question restatement: Using molecular orbital theory, predict how many unpaired electrons are in the B22– ion.
Option 4: '4' — This would imply four unpaired electrons. For a diatomic boron species, we must fill the bonding and antibonding MOs according to the 12 or 14 electron count of B2 or B2–/B22–, and determine spin occupancy. Four unpaired electrons is unlikely given typical MO ordering for B2-type diatomics, where electrons tend to pair up in lower MOs before occupying higher antibonding orbitals. This option overestimates the number of unpaired electrons for B22–.
Option 2: '2' — This suggests there are two unpaired electrons. In many boron diatomics and boron-containing ions, after filling the σ2s, σ*2s, π2p (degenerate), and σ2p orbitals with the available electrons, a remainder can lead to two unpaired spins, depending on the exact MO arrangement and electron count for B22–. Given the added electron in the anion, the occupation can yield two unpaired electrons in a π* or similar set, making this a plausible outcome.
Option 3: '3' — Three unpaired electrons would indicate an odd distribution of spin across MOs, which is less common for closed-shell or near-closed-shell diatomic boron species like B22–. The electron pairing pattern in typical B–B MO schemes tends to favor even numbers of unpaired electrons unless there is an odd electron count, which is not the case here with a 22– charge context that still adheres to even electron counts in a stable diatomic MO framework.
Option 1: '1' — A single unpaired electron would imply a radical with an odd number of total electrons in the bonding situation, but B22– would contribute an even total number of valence electrons when considering the diatomic combination and the extra electron. A single unpaired electron is inconsistent with the standard electron count for B22– in MO theory, which usually yields either 0, 2, or more unpaired electrons depending on orbital filling; 1 is generally unlikely for a closed-shell-like two-atom system with paired electrons.
Option 5: '0' — Zero unpaired electrons would correspond to a completely paired MO configuration, i.e., a closed-shell scenario. However, for B22– the extra electron often populates a higher-energy antibonding or degenerate set, leading to at least one unpaired electron in many plausible MO orderings. Therefore, this option is less consistent with typical MO fills for B22– and known trends in boron diatomic anions.
Summary: Considering the electron count for B22– and the common MO filling patterns for diatomic boron species, two unpaired electrons is the most consistent outcome among the provided options, with other counts (0, 1, 3, or 4) facing interpretive or factual inconsistencies in standard MO predictions for this ion.

Using the molecular orbital theory, predict how many unpaired electrons are in the B22– ion.

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