Write electron configurations for the following ions, and determine which have noble-gas configurations: (a) \(\mathrm{Cd}^{2+}\) , \((\mathbf{b}) \mathrm{P}^{3-},(\mathbf{c}) \mathrm{Zr}^{4+},(\mathbf{d}) \mathrm{Ru}^{3+},(\mathbf{e}) \mathrm{As}^{3-},(\mathbf{f}) \mathrm{Ag}^{+}\)

Find the atomic numbers of the elements based on their symbols in the periodic table: Cd: 48 P: 15 Zr: 40 Ru: 44 As: 33 Ag: 47

Write the electron configurations for the neutral atoms using the periodic table and the standard method for writing electron configurations: Cd: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^{10}\) P: \(1s^2 2s^2 2p^6 3s^2 3p^3\) Zr: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^2\) Ru: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^7\) As: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^3\) Ag: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^1 4d^{10}\)

Cd²⁺: Remove two electrons from the highest-energy orbital, which is the 4d orbital: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^8\) P³⁻: Add three electrons to the highest-energy orbital, which is the 3p orbital: \(1s^2 2s^2 2p^6 3s^2 3p^6\) Zr⁴⁺: Remove four electrons from the highest-energy orbitals, starting with the 4d and then the 5s orbitals: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^0 4d^0\) Ru³⁺: Remove three electrons from the highest-energy orbitals, starting with the 4d and then the 5s orbitals: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^0 4d^4\) As³⁻: Add three electrons to the highest-energy orbital, which is the 4p orbital: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6\) Ag⁺: Remove one electron from the highest-energy orbital, which is the 5s orbital: \(1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^0 4d^{10}\)

The electron configurations of noble gases are complete with full energy levels, and their general form is (\(n-1\)d^{10})np^6, where \(n\) is the principal quantum number of the noble gases. In our adjusted electron configurations from Step 3, the following ions match the noble gas configurations: - P³⁻ matches the configuration of Ne (Z=10): \(1s^2 2s^2 2p^6\) - As³⁻ matches the configuration of Ar (Z=18): \(1s^2 2s^2 2p^6 3s^2 3p^6\) Conclusion: Only P³⁻ and As³⁻ ions have noble-gas configurations.