Problem 45 - A Complete Resource Book in Chemistry for JEE Main

Question

The correct order of ionic radii of \(\mathrm{Y}^{3+}, \mathrm{La}^{3+}, \mathrm{Eu}^{3+}\) and \(\mathrm{Lu}^{3+}\) is (a) \(\mathrm{Lu}^{3+}<\mathrm{Eu}^{3+}<\mathrm{La}^{3+}<\mathrm{Y}^{3+}\) (b) \(\mathrm{La}^{3+}<\mathrm{Eu}^{3+}<\mathrm{Lu}^{3+}<\mathrm{Y}^{3+}\) (c) \(\mathrm{Y}^{3+}<\mathrm{La}^{3+}<\mathrm{Eu}^{3+}<\mathrm{Lu}^{3+}\) (d) \(\mathrm{Y}^{3+}<\mathrm{Lu}^{3+}<\mathrm{Eu}^{3+}<\mathrm{La}^{3+}\)

Step-by-Step Solution

Answer

The correct order is (d) \(\mathrm{Y}^{3+}<\mathrm{Lu}^{3+}<\mathrm{Eu}^{3+}<\mathrm{La}^{3+}\).

Step 1: Understand the Concept

Ionic radii refer to the size of an ion. In lanthanide and transition metal series, as the atomic number increases, the ionic radii usually decrease due to increased nuclear charge pulling the electron cloud closer. This phenomenon is called the Lanthanide contraction.

Step 2: Analyze Each Ion

For \(_{39}^{89}\mathrm{Y^{3+}}\), a 3+ ion, it is a transition metal land smaller in size than its lanthanide counterparts. La (Lanthanum), Eu (Europium), and Lu (Lutetium) are lanthanides. Their ionic radii generally decrease across the series, from La to Lu.

Step 3: Order by Ionic Radii

The order of decreasing ionic radius for these ions should follow the trend that the radius decreases as we move from La to Lu: 1. \(_{57}^{138.91}\mathrm{La^{3+}}\) has the largest ionic radius as it's the first among the lanthanides.2. \(_{63}^{152}\mathrm{Eu^{3+}}\) has a slightly smaller ionic radius than La.3. \(_{71}^{174.97}\mathrm{Lu^{3+}}\) has the smallest among the lanthanide ionic radii. 4. \(_{39}^{89}\mathrm{Y^{3+}}\) would have a small ionic radius resembling more the end of the lanthanide series.

Step 4: Match with Given Options

From the ordering determined: 1. \(_{39}^{89}\mathrm{Y^{3+}}\) has a smaller ionic radius than \(_{71}^{174.97}\mathrm{Lu}^{3+}\).2. \(_{71}^{174.97}\mathrm{Lu^{3+}}\) smaller than \(_{63}^{152}\mathrm{Eu}^{3+}\).3. \(_{63}^{152}\mathrm{Eu^{3+}}\) smaller than \(_{57}^{138.91}\mathrm{La^{3+}}\). This correlates directly with option (d) Y< Lu < Eu < La.

Key Concepts

Lanthanide Contraction

When exploring the world of chemistry, particularly the lanthanide series, you'll encounter a fascinating phenomenon called the lanthanide contraction. This concept is crucial in determining the ionic radii of various elements. As you move from left to right across the lanthanide series on the periodic table, each element adds one more proton and one more electron inside the f-orbitals. However, something intriguing happens: the effective nuclear charge pulling on the electron cloud increases steadily.
This results in a gradual decrease in the ionic radius despite the increasing electronic population. This is different from other periods where increased shielding typically accompanies increase in size.

• The electrons in the 4f orbitals do not shield the outer electrons effectively.
• This results in stronger attraction between the nucleus and the outermost electrons.
• The consequence is a smaller ionic radii as you proceed through the lanthanide series from Lanthanum (La) to Lutetium (Lu).

Understanding the lanthanide contraction helps explain why lutetium (Lu) is smaller than europium (Eu), which is smaller than lanthanum (La). Each step forward in the lanthanide series leads to a slight decrease in ionic size.

Transition Metals

Transition metals form another captivating category of elements well worth understanding. Found in the d-block of the periodic table, transition metals have exotic properties that set them apart from other elements. Their electron structures involve the filling of d orbitals, resulting in unique characteristics like various oxidation states, magnetic properties, and complex formation abilities.
Some key features of transition metals include:

• High melting and boiling points and metallic nature.
• The presence of partially-filled d-orbitals.
• The ability to form colored compounds.
• Diverse oxidation states, which arise from the involvement of both d and s electrons in bonding.

Yttrium (Y), although not a lanthanide, acts similar to other transition metals. Its role as a 3+ charged ion reflects its participation in many chemical reactions and behaviors you might see with other transition metals. Notably, yttrium's size in its ionic form is fairly small compared to lanthanide ions, heavily influenced by the nearby lanthanide contraction forces but exhibiting its own unique transition metal characteristics.

Ionic Size Comparison

Comparing ionic radii requires us to look beyond simple chemical formulas and deeply understand the intricacies of atomic structure. Ionic size is critical in comprehending how elements interact and bond with one another. While determining ionic sizes, especially within groups such as lanthanides and transition metals, consider the interplay of multiple factors.
As highlighted in ionic size comparisons, lanthanides tend to show a decreasing trend in their ionic radii due to lanthanide contraction. Similarly, transition metals typically decrease in size from left to right due to increased nuclear charge.
Let's break this down:

• Lanthanum (La) usually has the largest ionic size among the 3+ ions in the lanthanide series.
• Next in line would be europium (Eu) and lutetium (Lu), reflecting the decreasing trends due to lanthanide contraction.
• Yttrium (Y), being a transition metal, is smaller in its 3+ ionic form due to a high effective nuclear charge that pulls electrons inward effectively.

In a broader sense, understanding these comparisons helps explain how transition metals and lanthanides fit into the chemical puzzle. Observing their ionic sizes provides insights into their reactivity patterns, placement in compounds, and roles in technological applications.