Write the ground-state electron configuration for each of the following atoms or ions. Which have a valence-shell octet? (a) \(\overline{\mathrm{Ar}}\) (b) \(\mathrm{Na}^{+}\) (c) \(\mathrm{C}^{2-}\) (d) \(\mathrm{O}^{2-}\) (e) \(\mathrm{Ca}^{2+}\)

To determine the ground-state electron configuration, it's important to remember these three principles: - Aufbau Principle: Electrons are placed in orbitals in order of increasing energy (lowest energy levels first). - Hund's Rule: Electrons occupy orbitals of the same energy level (degenerate orbitals) in a way that maximizes the total number of parallel spins. - Pauli Exclusion Principle: No more than 2 electrons can occupy the same orbital, and these 2 electrons must have opposite spins.

Now we will find the ground-state electron configurations for each atom/ion using the above principles. Here are the atomic numbers of each element corresponding to the protons, which equals the number of electrons in a neutral atom: - Argon (Ar): 18 - Sodium (Na): 11 - Carbon (C): 6 - Oxygen (O): 8 - Calcium (Ca): 20 For each element, we have to adjust the number of electrons according to the given ion charge. (a) \(\overline{\mathrm{Ar}}\) (neutral): 18 electrons Electron configuration: \(\mathrm{1s^{2}\,2s^{2}\,2p^{6}\,3s^{2}\,3p^{6}}\) (b) \(\mathrm{Na}^{+}\): 10 electrons (lost 1 electron) Electron configuration: \(\mathrm{1s^{2}\,2s^{2}\,2p^{6}}\) (c) \(\mathrm{C}^{2-}\): 8 electrons (gained 2 electrons) Electron configuration: \(\mathrm{1s^{2}\,2s^{2}\,2p^{4}}\) (d) \(\mathrm{O}^{2-}\): 10 electrons (gained 2 electrons) Electron configuration: \(\mathrm{1s^{2}\,2s^{2}\,2p^{6}}\) (e) \(\mathrm{Ca}^{2+}\): 18 electrons (lost 2 electrons) Electron configuration: \(\mathrm{1s^{2}\,2s^{2}\,2p^{6}\,3s^{2}\,3p^{6}}\)

To determine which atoms or ions have a valence-shell octet, we need to check the outermost shell (highest principal quantum number) of each atom/ion: (a) \(\overline{\mathrm{Ar}}\): Valence-shell (n=3) has 8 electrons (3s² and 3p⁶), so it has an octet. (b) \(\mathrm{Na}^{+}\): Valence-shell (n=2) has 8 electrons (2s² and 2p⁶), so it has an octet. (c) \(\mathrm{C}^{2-}\): Valence-shell (n=2) has 6 electrons (2s² and 2p⁴), so it does not have an octet. (d) \(\mathrm{O}^{2-}\): Valence-shell (n=2) has 8 electrons (2s² and 2p⁶), so it has an octet. (e) \(\mathrm{Ca}^{2+}\): Valence-shell (n=3) has 8 electrons (3s² and 3p⁶), so it has an octet. Therefore, the atoms or ions having a valence-shell octet are: \(\overline{\mathrm{Ar}}\), \(\mathrm{Na}^{+}\), \(\mathrm{O}^{2-}\), and \(\mathrm{Ca}^{2+}\).