Question

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

Short answer

All options (a, b, c) are in decreasing order by radius.

Step-by-step solution

Review the Concept of Atomic and Ionic Radius

The atomic radius is the distance from the center of the nucleus to the outermost electron shell of an atom. Generally, the atomic radius increases as we go down a group in the periodic table and decreases across a period from left to right. The ionic radius follows similar trends but depends on the charge of the ion. Cations (positively charged ions) have a smaller radius than their neutral atoms because they lose electrons, while anions (negatively charged ions) have a larger radius because they gain electrons.

Evaluate Option (a): Be, Mg, Ba

Beryllium (Be), magnesium (Mg), and barium (Ba) are alkaline earth metals located in Group 2 of the periodic table. As we move down the group from Be to Ba, the atomic size increases. Thus, the order of atomic radius in decreasing size is Ba, Mg, Be.

Evaluate Option (b): \(\mathrm{N}^{3-}, \mathrm{O}^{2-}, \mathrm{F}^{-}\)

Nitride (\(\mathrm{N}^{3-}\)), oxide (\(\mathrm{O}^{2-}\)), and fluoride (\(\mathrm{F}^{-}\)) are isoelectronic species, each having gained electrons. In isoelectronic species, the ion with the higher negative charge will have the largest radius due to increased electron-electron repulsion. Hence, the order is \(\mathrm{N}^{3-}\), \(\mathrm{O}^{2-}\), \(\mathrm{F}^{-}\) in decreasing radius.

Evaluate Option (c): \(\mathrm{Tl}^{3+}, \mathrm{Tl}^{2+}, \mathrm{Tl}^{+}\)

The ions \(\mathrm{Tl}^{3+}\), \(\mathrm{Tl}^{2+}\), and \(\mathrm{Tl}^{+}\) are cations of thallium, which lose electrons and become positively charged. The fewer the electrons lost, the larger the ionic radius. Therefore, the order in decreasing size of radius is \(\mathrm{Tl}^{+}\), \(\mathrm{Tl}^{2+}\), \(\mathrm{Tl}^{3+}\).

Determine Which Option is Correct

Compare the analysis of each option: \((a)\) is Ba, Mg, Be reflecting a decreasing order; \((b)\) is \(\mathrm{N}^{3-}\), \(\mathrm{O}^{2-}\), \(\mathrm{F}^{-}\), also decreasing; \((c)\) is \(\mathrm{Tl}^{+}\), \(\mathrm{Tl}^{2+}\), \(\mathrm{Tl}^{3+}\), again decreasing. Therefore, all options are in decreasing order.

Key concepts

Periodic Table Trends

Understanding trends in the periodic table helps us predict and explain the physical and chemical behavior of elements. One of these trends is the atomic radius. It is the distance from the nucleus of an atom to the edge of its outermost electron shell. This radius tends to increase as you move down a group in the periodic table because each row adds another electron shell. Conversely, as you move from left to right across a period, the atomic radius generally decreases because the increasing nuclear charge pulls the electron cloud closer to the nucleus.
This knowledge is essential when arranging elements or ions by size. For instance, in the exercise involving Beryllium (Be), Magnesium (Mg), and Barium (Ba), these elements belong to the same group (Group 2 - alkaline earth metals). Hence, the atomic size increases from Be to Ba. This is why the decreasing order of radius is Ba, Mg, Be.
These trends are fundamental to understanding element interactions and properties across the periodic table.

Isoelectronic Species

Isoelectronic species are atoms or ions that have the same number of electrons. Although they share an electron count, their nuclear charges differ, which influences their relative sizes. When comparing isoelectronic species, the key is their nuclear charge: the more protons in the nucleus, the stronger the attraction of the electrons to the nucleus, leading to a smaller radius.
Consider the example of nitride ( ^{3-} ), oxide ( ^{2-} ), and fluoride ( ^{-} ), which are isoelectronic, each having a total of 10 electrons. Among them, nitride has the most negative charge, indicating less nuclear attraction and thus, the largest size. Therefore, the decreasing order by size is ^{3-} , ^{2-} , ^{-} .
Understanding these comparisons helps in grasping concepts related to electron configurations and the properties of ions.

Cation and Anion Radius

The sizes of ions can be strikingly different from their parent atoms, and understanding the behavior of cations and anions will clarify this transformation. Cations, which are positively charged due to the loss of electrons, tend to be smaller than their neutral atoms. This size decrease occurs because losing electrons usually leads to a reduction in electron-electron repulsion and allows the remaining electrons to be pulled closer to the nucleus. In contrast, anions, negatively charged due to the gain of electrons, are typically larger than their corresponding neutral atoms. This size increase arises from greater electron repulsion within the electron cloud.
As illustrated in the exercise, ^{3+} , ^{2+} , and ^{+} are cations of thallium that decrease in size as more electrons are lost. So, the order is ^{+} , ^{2+} , ^{3+} , reflecting that fewer removed electrons mean a larger size.
Recognizing these size changes is vital for predicting the behavior of ions in chemical reactions and compounds.