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To determine the number of unpaired electrons in Lutetium (Lu) in the +3 oxidation state, we first need to understand its electronic configuration. Lutetium has an atomic number of 71. Therefore, its ground state electron configuration is: [Xe] 4f14 5d1 6s2
Lutetium in the +3 oxidation state means it has lost three electrons. These electrons are removed first from the outermost shell following the order of 6s and then 5d:
Thus, the electron configuration for Lu3+ is: [Xe] 4f14
Next, we look at the 4f sublevel, which is completely filled with 14 electrons. A completely filled sublevel has no unpaired electrons.
Thus, Lutetium in the +3 oxidation state has 0 unpaired electrons.