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 show a significant decrease from O^{2-} to Al^{3+} ; hence, option (d) is correct.

Step 1: Understanding Isoelectronic Species

Isoelectronic species are atoms or ions that have the same number of electrons. In this case, all given ions (0^{2-}, F^{-}, Na^{+}, Mg^{2+}, Al^{3+} ) have the same number of electrons as 10 electrons.

Step 2: Analyzing Effective Nuclear Charge

The effective nuclear charge (Z_{eff} ) refers to the net positive charge experienced by electrons in a poly-electron atom or ion. As you move from O^{2-} to Al^{3+} , the number of protons increases, leading to a higher Z_{eff} which means the nucleus pulls the electrons closer.

Step 3: Evaluating Ionic Radii

The ionic radius is affected by Z_{eff} . With the increase in Z_{eff} across the ions (from O^{2-} to Al^{3+} ), the electrons are pulled more tightly toward the nucleus, resulting in a decrease in the ionic radius.

Step 4: Conclusion on Radius Trend

Because the effective nuclear charge increases from O^{2-} to Al^{3+} , leading to stronger attraction between the nucleus and electrons, the ionic radius decreases. Thus, the ionic radii show a significant decrease from O^{2-} to Al^{3+} .

Key Concepts

Effective Nuclear Charge

Effective nuclear charge, often denoted as \( Z_{eff} \), is a vital concept in understanding atomic and ionic behavior. It is the net positive charge experienced by an electron in a multi-electron atom. Essentially, it measures how strongly the nucleus attracts electrons.

Here’s the intuitive part: more protons in the nucleus means a greater pull on the electrons. As you move across a period on the periodic table, \( Z_{eff} \) increases due to the addition of protons while the electron shielding effect remains relatively constant. This increased nuclear charge means electrons are drawn closer to the nucleus, reducing the size of the electron cloud.

In the context of isoelectronic ions such as \( \mathrm{O}^{2-} \), \( \mathrm{F}^{-} \), \( \mathrm{Na}^{+} \), \( \mathrm{Mg}^{2+} \), and \( \mathrm{Al}^{3+} \), each ion has the same number of electrons. However, \( Z_{eff} \) changes due to increasing proton number from oxygen to aluminum. This explains why their physical sizes, or ionic radii, decrease as you move from \( \mathrm{O}^{2-} \) to \( \mathrm{Al}^{3+} \), despite having the same number of electrons.

Ionic Radius

The ionic radius is the measure of an atom's ion size, and it changes based on the effective nuclear charge and electron configuration. In isoelectronic species, changes in ionic radii are observed due to differences in effective nuclear charge.

Here's how it works in simple terms: with more protons pulling on the same number of electrons, the electrons are pulled closer to the nucleus, reducing the ionic radius. This means that as you go from \( \mathrm{O}^{2-} \) to \( \mathrm{Al}^{3+} \), the ionic radius gets smaller.

• The larger ions are those with fewer protons for a given electron pack, so \( \mathrm{O}^{2-} \) has the largest radius.
• Conversely, \( \mathrm{Al}^{3+} \) has the smallest size because the same number of electrons experience a greater pull from more protons.

Remember, the trend in ionic size for isoelectronic species is dictated by the effective nuclear charge – more protons, smaller ions.

Electron Configuration

Electron configuration refers to the arrangement of electrons in an atom or ion's electron orbitals. For isoelectronic species, identical electron configuration is the defining feature.

All of the given ions \( \mathrm{O}^{2-} \), \( \mathrm{F}^{-} \), \( \mathrm{Na}^{+} \), \( \mathrm{Mg}^{2+} \), and \( \mathrm{Al}^{3+} \) have the same electron configuration of \([ \mathrm{Ne} ]\), comprising 10 electrons. This uniform configuration explains why they are described together even though they belong to different elements.

This similarity in electron count leads to the unique observation that, despite different origins, these ions behave similarly in how they pack their electrons in the available space. Nevertheless, it's the differences in effective nuclear charge that define their varied behaviors in terms of size and reactivity across the period.