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

(d) A significant decrease from \( \mathrm{O}^{2-} \) to \( \mathrm{Al}^{3+} \).

Step 1: Understanding the term 'Isoelectronic'

The term 'isoelectronic' refers to ions and atoms that have the same number of electrons. In this problem, the ions \( \mathrm{O}^{2-} \), \( \mathrm{F}^{-} \), \( \mathrm{Na}^{+} \), \( \mathrm{Mg}^{2+} \), and \( \mathrm{Al}^{3+} \) all have the same electron configuration as neon (\( \mathrm{Ne} \)), which is 10 electrons.

Step 2: Ordering by Effective Nuclear Charge

Although these ions are isoelectronic, they have different numbers of protons in their nuclei. The effective nuclear charge increases from \( \mathrm{O}^{2-} \) (8 protons) to \( \mathrm{F}^{-} \) (9 protons), \( \mathrm{Na}^{+} \) (11 protons), \( \mathrm{Mg}^{2+} \) (12 protons), and finally \( \mathrm{Al}^{3+} \) (13 protons).

Step 3: Relation Between Effective Nuclear Charge and Ionic Radius

The greater the effective nuclear charge, the more strongly the electrons are pulled toward the nucleus, resulting in a smaller ionic radius. As effective nuclear charge increases, the ionic radius generally decreases.

Step 4: Comparing Ionic Radii

Starting from \( \mathrm{O}^{2-} \) to \( \mathrm{Al}^{3+} \), the number of protons increases, leading to a stronger pull on the same number of electrons. This results in a progressive decrease in ionic radii.

Step 5: Determine the Trend Among the Options

The statement "a significant decrease from \( \mathrm{O}^{2-} \) to \( \mathrm{Al}^{3+} \)" matches our understanding of the trend in ionic radii due to increasing effective nuclear charge.

Key Concepts

Effective Nuclear Charge

When we discuss isoelectronic ions, understanding effective nuclear charge is crucial. Effective nuclear charge is essentially the net positive charge experienced by electrons. Although isoelectronic ions have the same number of electrons, they differ in the number of protons in their nucleus. This affects how strongly electrons are attracted to the nucleus.For example, in our exercise, ions like \( \mathrm{O}^{2-} \) and \( \mathrm{Al}^{3+} \) are isoelectronic but vary in proton number. \( \mathrm{O}^{2-} \) has 8 protons, while \( \mathrm{Al}^{3+} \) has 13 protons. The greater the number of protons, the greater the effective nuclear charge, because the added positive charge increases the attraction between the nucleus and the surrounding electrons. This concept helps us understand why as we move from \( \mathrm{O}^{2-} \) to \( \mathrm{Al}^{3+} \), the effective nuclear charge consistently increases.

Ionic Radius Trend

The ionic radius trend is closely related to the effective nuclear charge. A higher effective nuclear charge means electrons are pulled closer to the nucleus, resulting in a smaller ionic radius.In the set of isoelectronic ions \( \mathrm{O}^{2-} \), \( \mathrm{F}^{-} \), \( \mathrm{Na}^{+} \), \( \mathrm{Mg}^{2+} \), and \( \mathrm{Al}^{3+} \), we see a fascinating trend. Even though all have the same electron configuration, their ionic radii vary. As we move across this series from \( \mathrm{O}^{2-} \) to \( \mathrm{Al}^{3+} \), each ion has progressively more protons:

• \( \mathrm{O}^{2-} \): 8 protons
• \( \mathrm{F}^{-} \): 9 protons
• \( \mathrm{Na}^{+} \): 11 protons
• \( \mathrm{Mg}^{2+} \): 12 protons
• \( \mathrm{Al}^{3+} \): 13 protons

With this increase in protons, the effective nuclear charge intensifies, pulling the electrons closer. Therefore, the ionic radius decreases as you progress from \( \mathrm{O}^{2-} \) to \( \mathrm{Al}^{3+} \). This helps explain the observed significant decrease in ionic radii across these ions.

Electron Configuration

Electron configuration is the arrangement of electrons in an atom or ion, often in terms of energy levels and sublevels. One exciting aspect of the ions \( \mathrm{O}^{2-} \), \( \mathrm{F}^{-} \), \( \mathrm{Na}^{+} \), \( \mathrm{Mg}^{2+} \), and \( \mathrm{Al}^{3+} \) is that they are isoelectronic, which means they all have the same electron configuration as neon (\( \mathrm{Ne} \)), comprising 10 electrons.Each of these ions has adjusted its electron count to achieve a stable electron configuration, similar to the noble gas, neon:

• \( \mathrm{O}^{2-} \): Gains two electrons
• \( \mathrm{F}^{-} \): Gains one electron
• \( \mathrm{Na}^{+} \): Loses one electron
• \( \mathrm{Mg}^{2+} \): Loses two electrons
• \( \mathrm{Al}^{3+} \): Loses three electrons

This uniform electron configuration results in the ions being neutral in terms of electron count, albeit with differing nuclear charges. It highlights how elements strive for stable, energy-efficient arrangements, resulting in isoelectronic species across the periodic table. The principles of electron configuration not only aid in predicting ionic forms but also in understanding the chemical behavior of elements.