Select the smaller member of each pair. (a) \(\mathrm{N}\) and \(\mathrm{N}^{3-}\) (b) \(\mathrm{Ba}\) and \(\mathrm{Ba}^{2+}\) (c) Se and \(\mathrm{Se}^{2-}\) (d) \(\mathrm{Co}^{2+}\) and \(\mathrm{Co}^{3+}\)

Atoms are made up of protons, electrons, and neutrons. The positively charged protons are in the nucleus, while the negatively charged electrons are in the electron cloud surrounding the nucleus. The size of an atom is determined by the electron cloud, as it makes up the majority of the volume of the atom. When the atom loses or gains electrons, the size of the electron cloud changes, leading to a difference in atomic size or ionic size. In general, the size of an ion depends on several factors, such as the number of protons in the nucleus, the distribution of electrons in the electron cloud, and the effective nuclear charge.

Now we will look at each pair and apply the general rules for atomic and ionic sizes to determine which one is smaller: (a) N and N^3-: Nitrogen (N) is a neutral atom with 7 protons and 7 electrons, while N^3- is an anion formed by the addition of 3 electrons to a nitrogen atom, making it a total of 10 electrons. Since the number of electrons has increased, the electron-electron repulsion will also increase, causing the electron cloud to expand. Therefore, N^3- is larger than N. So, N is the smaller member of this pair. (b) Ba and Ba^2+: Barium (Ba) is a neutral atom with 56 protons and 56 electrons, while Ba^2+ is a cation formed by the removal of 2 electrons from a barium atom, leaving it with 54 electrons. As electrons are removed from the electron cloud, the net charge of the nucleus remains the same (since protons are not changing), leading to a stronger effective nuclear charge. This pulls the remaining electrons closer to the nucleus, resulting in a smaller size for Ba^2+. Thus, Ba^2+ is the smaller member of this pair. (c) Se and Se^2-: Selenium (Se) is a neutral atom with 34 protons and 34 electrons, while Se^2- is an anion formed by the addition of 2 electrons to a selenium atom, making it a total of 36 electrons. Similar to the situation with nitrogen, adding electrons increases the electron-electron repulsion and leads to a larger size for Se^2-. Thus, Se is the smaller member of this pair. (d) Co^2+ and Co^3+: Co^2+ and Co^3+ are both cobalt cations with different charges. Co^2+ is formed by the removal of 2 electrons from a cobalt atom, while Co^3+ is formed by the removal of 3 electrons from the atom. As we go from Co^2+ to Co^3+, there are fewer electrons left for the same number of protons. This results in stronger effective nuclear charge and pulling the remaining electrons closer to the nucleus. Therefore, Co^3+ is smaller than Co^2+, and Co^3+ is the smaller member of this pair.

In summary: (a) Smaller member: N (b) Smaller member: Ba^2+ (c) Smaller member: Se (d) Smaller member: Co^3+