Write electron configurations for the following ions. a. \(\mathrm{Ni}^{2+}\) b. \(\mathrm{Cd}^{2+}\) c. \(\mathrm{Zr}^{3+}\) and \(\mathrm{Zr}^{4+}\) d. \(\mathrm{Os}^{2+}\) and \(\mathrm{Os}^{3+}\)

We can find the atomic numbers of each element by referring to the periodic table. The atomic number represents the number of protons (and electrons in a neutral atom) in the element: a. \(\mathrm{Ni}\): Atomic number is 28 b. \(\mathrm{Cd}\): Atomic number is 48 c. \(\mathrm{Zr}\): Atomic number is 40 d. \(\mathrm{Os}\): Atomic number is 76

Next, use the atomic number to determine the ground-state electron configuration for the neutral atoms of each element. The electron configuration will be in the form of orbital symbols and superscripts representing the number of electrons in each orbital: a. \(\mathrm{Ni}\): \([\mathrm{Ar}] \, 4\mathrm{s}^2 \, 3\mathrm{d}^8 \) b. \(\mathrm{Cd}\): \([\mathrm{Kr}] \, 5\mathrm{s}^2 \, 4\mathrm{d}^{10} \) c. \(\mathrm{Zr}\): \([\mathrm{Kr}] \, 5\mathrm{s}^2 \, 4\mathrm{d}^2 \, 4\mathrm{f}^0 \,\) (\(4\mathrm{f}\) is included to show that \(\mathrm{Zr}\) is in the \(\mathrm{d}\)-block) d. \(\mathrm{Os}\): \([\mathrm{Xe}] \, 6\mathrm{s}^2 \, 4\mathrm{f}^{14} \, 5\mathrm{d}^6\)

Now, we need to adjust each electron configuration for the ions provided by removing the appropriate number of electrons from the valence shell. Valence electrons are the outermost electrons that are removed first when forming cations: a. \(\mathrm{Ni}^{2+}\): \([\mathrm{Ar}] \, 4\mathrm{s}^0 \,3\mathrm{d}^8 \rightarrow [\mathrm{Ar}] \, 3\mathrm{d}^8\) b. \(\mathrm{Cd}^{2+}\): \([\mathrm{Kr}] \, 5\mathrm{s}^0 \,4\mathrm{d}^{10} \rightarrow [\mathrm{Kr}] \, 4\mathrm{d}^{10}\) c. \(\mathrm{Zr}^{3+}\): \([\mathrm{Kr}] \, 5\mathrm{s}^0 \,4\mathrm{d}^0 \, 4\mathrm{f}^0 \rightarrow [\mathrm{Kr}]\) \(\mathrm{Zr}^{4+}\): \([\mathrm{Kr}] \,5\mathrm{s}^0 \, 4\mathrm{d}^0 \, 4\mathrm{f}^0 \rightarrow [\mathrm{Kr}]\) d. \(\mathrm{Os}^{2+}\): \([\mathrm{Xe}] \, 6\mathrm{s}^0 \,4\mathrm{f}^{14} \, 5\mathrm{d}^6 \rightarrow [\mathrm{Xe}] \, 4\mathrm{f}^{14} \, 5\mathrm{d}^6\) \(\mathrm{Os}^{3+}\): \([\mathrm{Xe}] \, 6\mathrm{s}^0 \,4\mathrm{f}^{14} \, 5\mathrm{d}^5 \rightarrow [\mathrm{Xe}] \, 4\mathrm{f}^{14} \, 5\mathrm{d}^5\)