Problem 145 - A Complete Resource Book in Chemistry for JEE Main

Question

The radius of \(\mathrm{La}^{3+}\) (atomic number \(=57\) ) is \(1.06 \mathrm{~A}\). Which one of the following given values will be closest to the radius of \(\mathrm{Lu}^{3+}\) (atomic number \(=71\) )? [2003] (a) \(0.85 \mathrm{~A}\) (b) \(1.06 \mathrm{~A}\) (c) \(1.40 \mathrm{~A}\) (d) \(1.60 \mathrm{~A}\)

Step-by-Step Solution

Answer

The radius of \\( \mathrm{Lu}^{3+} \\) is closest to 0.85 Å due to lanthanide contraction.

Step 1: Understand the Periodicity of Lanthanides

Lanthanides are elements from La to Lu, with increasing atomic numbers from 57 to 71. As atomic number increases, effective nuclear charge also increases, leading to Lanthanide contraction.

Step 2: Explain Lanthanide Contraction

Lanthanide contraction refers to the gradual reduction in the atomic and ionic sizes of lanthanides as you move from La to Lu due to poor shielding effect of 4f electrons.

Step 3: Analyze the Given Ion Radii

The ionic radii of \( \mathrm{La}^{3+} \) is given as 1.06 Å. Due to the lanthanide contraction effect, \( \mathrm{Lu}^{3+} \) should be smaller in size than 1.06 Å.

Step 4: Choose the Closest Value

From the options given (a) 0.85 Å, (b) 1.06 Å, (c) 1.40 Å, and (d) 1.60 Å, option (a) 0.85 Å is smaller than 1.06 Å and is the closest estimate of \( \mathrm{Lu}^{3+} \) considering the lanthanide contraction.

Key Concepts

Periodicity in Lanthanides

Lanthanides are a series of elements in the periodic table ranging from lanthanum (La) to lutetium (Lu). These elements are known for their remarkable periodicity – a pattern of properties that repeats itself across the series. As you progress from La to Lu, the atomic number increases, which means there are more protons in the nucleus and more electrons around it. This results in changes in various properties such as ionic size, oxidation states, and electronic configuration. Understanding this periodicity is crucial as it influences the chemical behavior of lanthanides.
The most notable pattern is the contraction of atomic and ionic radii, known as lanthanide contraction. This contraction plays a significant role in determining properties and reactions of lanthanides and contributes to their similarities with other rare earth elements. Such periodic patterns make lanthanides a unique and interesting group to study in the field of chemistry.

Ionic Radii

The ionic radii of lanthanides change in a predictable manner across the series. In general, as you move from La to Lu, the ionic radii decrease. This is due to the lanthanide contraction. For instance, the ionic radius of La\(^{3+}\) is 1.06 Å, but by the time you reach Lu\(^{3+}\), this radius is down to about 0.85 Å.
This decrease in size is significant because it affects how these ions pack into crystal structures and interact with other ions. Smaller ions lead to stronger ionic bonds and might also affect the solubility and stability of compounds containing lanthanides. Understanding ionic radii is essential for predicting the behavior of lanthanide ions in various chemical reactions and processes.

Effective Nuclear Charge

Effective nuclear charge is a key factor in understanding lanthanide contraction. It represents the net positive charge experienced by electrons in an atom. More simply, it's the actual nuclear charge minus the shielding effect caused by other electrons. As we move across the lanthanide series, the effective nuclear charge experienced by the outer electrons increases.
This happens because while new electrons are added to the f subshell, which does not shield very effectively, their positive nuclear charge pulls the electron cloud tighter, leading to a smaller atomic and ionic size. This increase in effective nuclear charge across the lanthanides is what causes their gradual reduction in radius – the hallmark of lanthanide contraction.

Shielding Effect

The shielding effect describes how inner electrons can shield outer electrons from the full positive charge of the nucleus. In lanthanides, the 4f electrons are not good at shielding one another. This poor shielding is a critical factor in the lanthanide contraction.
As more protons are added to the nucleus from La to Lu, the nuclear charge increases, pulling the outer electrons closer. However, the f-electrons do a poor job of offsetting this charge, which means each successive ion in the series is smaller than the last. This poor shielding contributes to the increasing effective nuclear charge and the reduction in size of the lanthanides, making it a vital part of understanding their periodic properties.