Problem 76 - A Complete Resource Book in Chemistry for JEE Main

Question

The ions \(\mathrm{O}^{2-}, \mathrm{F}^{-}, \mathrm{Na}^{+}, \mathrm{Mg}^{2+}\) and \(\mathrm{Al}^{3+}\) are isoelectronic. Their ionic radii show: (a) an increase from \(\mathrm{O}^{2-}\) to \(\mathrm{F}^{-}\)and then decrease from \(\mathrm{Na}^{+}\)to \(\mathrm{Al}^{3+}\) (b) an decrease from \(\mathrm{O}^{2-}\) to \(\mathrm{F}^{-}\)and then increase from \(\mathrm{Na}^{+}\)to \(\mathrm{Al}^{3+}\) (c) a significant increase from \(\mathrm{O}^{2-}\) to \(\mathrm{Al}^{3+}\) (d) a significant decrease from \(\mathrm{O}^{2-}\) to \(\mathrm{Al}^{3+}\)

Step-by-Step Solution

Answer

The ionic radii significantly decrease from \(\mathrm{O}^{2-}\) to \(\mathrm{Al}^{3+}\), corresponding to option (d).

Step 1: Understand Isoelectronic Species

Isoelectronic species are ions or atoms that have the same number of electrons. In this case, all the given ions—\(\mathrm{O}^{2-}, \mathrm{F}^{-}, \mathrm{Na}^{+}, \mathrm{Mg}^{2+}\), and \(\mathrm{Al}^{3+}\)—are isoelectronic as they each have 10 electrons.

Step 2: Consider Nuclear Charge

For isoelectronic species, the number of protons (or nuclear charge) affects the ionic size. The more protons an ion has, the greater the pull on the electrons, leading to a decrease in ionic radius.

Step 3: Order the Ions by Increasing Nuclear Charge

Arrange the ions by their increasing nuclear charge (number of protons): \(\mathrm{O}^{2-}, \mathrm{F}^{-}, \mathrm{Na}^{+}, \mathrm{Mg}^{2+}, \mathrm{Al}^{3+}\). Since \(\mathrm{O}\) has 8 protons and \(\mathrm{Al}\) has 13 protons, \(\mathrm{Al}^{3+}\) will experience the most effective nuclear charge.

Step 4: Relation Between Nuclear Charge and Ionic Radius

For isoelectronic ions, as nuclear charge increases, ionic radius decreases. Hence, the ionic radius will decrease from \(\mathrm{O}^{2-}\) to \(\mathrm{Al}^{3+}\).

Step 5: Find the Correct Statement

According to Step 4, the ionic radii decrease steadily from \(\mathrm{O}^{2-}\) to \(\mathrm{Al}^{3+}\). Therefore, the significant decrease matches choice (d).

Key Concepts

Ionic Radius

The ionic radius is the measure of an ion's size, specifically the effective distance from the nucleus to the boundary of the surrounding cloud of electrons. Understanding ionic radius is crucial when studying how atoms form ions by either losing or gaining electrons. The ionic radius isn't a fixed point, but rather an average distance, impacted by several factors, such as the number of electrons surrounding the atom and the charge of the ion itself.

For instance, in isoelectronic species, which have the same number of electrons, like \(\mathrm{O}^{2-}, \mathrm{F}^{-}, \mathrm{Na}^{+}, \mathrm{Mg}^{2+}\, \text{and} \, \mathrm{Al}^{3+}\:\) the ionic radius changes based on how tightly the electrons are held by the nucleus. As the effective nuclear charge increases, the electrons are pulled in more closely. Thus, as nuclear charge increases across the series, the ionic radius generally decreases.

Nuclear Charge

Nuclear charge refers to the total charge of the protons within the nucleus, which fundamentally dictates how tightly electrons are held by an atom or ion. In simple terms, the nuclear charge is the atomic number since each proton carries a +1 charge.

For isoelectronic species, which have an identical number of electrons, differences in the nuclear charge are significant for determining their physical properties. Since electrons are drawn towards the positive charge in the nucleus, a higher nuclear charge results in a stronger pull inward. This causes the electrons to be closer to the nucleus, resulting in a smaller ionic radius. Thus, with an increase in nuclear charge from \(\mathrm{O}^{2-}\) (with 8 protons) to \(\mathrm{Al}^{3+}\) (with 13 protons), we see the ionic radii decrease due to a greater inward pull on the electron cloud.

Ionic Size

Ionic size, or radius, is a pivotal concept, especially for students learning about chemical bonding and atomic structure. The size of an ion is determined by the number of protons in the nucleus and the electron configuration surrounding it. As electrons are lost or gained to form positive or negative ions, the size changes accordingly.

For positive ions like \(\mathrm{Na}^{+}\) or \(\mathrm{Mg}^{2+}\), losing electrons typically results in a smaller ionic size compared to their neutral atoms because there are fewer electron-electron repulsions and the electron cloud is drawn closer to the nucleus. Conversely, negative ions have gained electrons, leading to a larger ionic size as the electron cloud expands due to increased repulsion among the additional electrons. However, within a series of isoelectronic ions such as those mentioned, the varying nuclear charge is the deciding factor for ionic size differences, resulting in a decrease across the series from \(\mathrm{O}^{2-}\) to \(\mathrm{Al}^{3+}\).

Periodic Trends

Periodic trends refer to the patterns observed in the properties of elements as you move across a period or down a group in the periodic table. One prominent trend is the change in atomic and ionic sizes. As you move across a period, each element gains one more proton, which in turn increases the nuclear charge, pulling the electron cloud more tightly, and thus reducing the size.

A perfect scenario to observe this is with isoelectronic species. Although these ions have the same number of electrons, their increasing nuclear charge as elements progress across a period leads to a decrease in ionic size. This trend not only helps in understanding the size of ionic species but also in predicting reactivity and bonding characteristics of elements. Mastering these trends provides a foundation for further studies into chemistry and molecular interactions.