In which of these are the species written in decreasing radius? (a) \(\mathrm{Be}, \mathrm{Mg}, \mathrm{Ba}\) (b) \(\mathrm{N}^{3-}, \mathrm{O}^{2-}, \mathrm{F}^{-}\) (c) \(\mathrm{Tl}^{3+}, \mathrm{Tl}^{2+}, \mathrm{Tl}^{+}\)

The periodic table is much more than just a table with elements; it is a roadmap to understanding the behavior and properties of those elements. One fundamental aspect to grasp is the concept of periodic table groups. These are the columns in the periodic table, and they play a significant role in determining element characteristics such as atomic size.

Elements in the same group have similar properties because they have the same number of electrons in their outermost shell, also known as valence electrons. These electrons are the ones involved in chemical reactions. As you move down a group, elements gain an additional electron shell, making the atom larger because the outermost electrons are at higher energy levels and further away from the nucleus. This is why, in group 2 of the periodic table, barium (Ba) has a larger atomic radius than magnesium (Mg), which in turn is larger than beryllium (Be).

When an atom gains or loses electrons, it becomes an ion and its size changes; this size is referred to as the ionic radius. The ionic radius trend is a bit more complex than that of the atomic radius because it is affected not only by the number of electron shells but also by the number of electrons relative to protons after ionization.

Generally, negatively charged ions (anions) are larger than their parent atoms because the addition of electrons increases electron-electron repulsion, which makes the electron cloud expand. On the other hand, positively charged ions (cations) are usually smaller than their parent atoms due to the loss of electron(s) and hence reduced electron-electron repulsion, allowing the remaining electrons to be pulled closer to the nucleus.

In exercise (b), Nitride ion () has 10 electrons and 7 protons, Oxide ion (O2-) has 10 electrons and 8 protons, and Fluoride ion (F-) has 10 electrons and 9 protons. Here, as the number of protons increases while the number of electrons remains the same, the nucleus's ability to pull the electron cloud closer increases, thereby decreasing the ionic radius.

The term electron configuration refers to the distribution of electrons of an atom or ion in atomic orbitals. This configuration plays a critical role in determining an atom's chemical and physical properties, including atomic and ionic size. Electron configuration follows a set of principles and rules, such as the Aufbau principle, Pauli exclusion principle, and Hund’s rule.

In the context of ionic size, when an atom loses an electron to form a cation, if that electron is lost from a valence shell, this can lead to a 'contraction' of the ionic radius. In the case of Thallium (Tl) ions in exercise (c), as the ion becomes more positively charged from Tl+ to Tl+ to Tl3+, it loses more electrons, and the overall size of the ion decreases as the remaining electrons experience a stronger effective nuclear charge. This is because with fewer electrons, there is less electron-electron repulsion counteracting the pull of the positive nucleus, resulting in a smaller ionic radius for the higher positively charged ions.