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Chapter 7: Problem 184

We expect the atomic radius to increase going down a group in the periodic table. Can you suggest why the atomic radius of hafnium breaks this rule? (See data below.) $$\begin{array}{llll}{\mathrm{Sc}} & {157} & {\mathrm{Ti}} & {147.7} \\\ {\mathrm{Y}} & {169.3} & {\mathrm{Zr}} & {159.3} \\ {\mathrm{La}} & {191.5} & {\mathrm{Hf}} & {147.6}\end{array}$$

Short Answer

Expert verified
The deviation from the general trend of increasing atomic radii in the case of Hafnium can be attributed to the 'lanthanide contraction.' This phenomenon occurs due to the weak shielding effect of the 4f electron shell, resulting in an increased effective nuclear charge and a smaller atomic radius for Hafnium.

Step by step solution

01

Understand the periodic trend of atomic radii

When moving down a group in the periodic table, the number of shells (n) in an atom increases, meaning more electrons are being added in each shell further away from the nucleus. This generally results in an increase in atomic radii since the electrons are occupying more space.
02

Analyze the given data and identify the pattern

We have been given the following atomic radii for different elements in the same group: Scandium (Sc) - \(157\) Titanium (Ti) - \(147.7\) Yttrium (Y) - \(169.3\) Zirconium (Zr) - \(159.3\) Lanthanum (La) - \(191.5\) Hafnium (Hf) - \(147.6\) Looking at the given data, we can observe a general trend of increasing atomic radii when moving down the group (from Sc to La). However, Hafnium breaks this rule as its atomic radius is smaller than that of Lanthanum.
03

Determine the cause of the deviation from the trend

The deviation from the general trend in the case of Hafnium can be attributed to the 'lanthanide contraction.' This phenomenon occurs due to the weak shielding effect of the 4f electron shell. When moving across the period from Lanthanum to Hafnium, electrons are being added to the 4f shell, but their shielding effect is weak, which results in increased effective nuclear charge and, consequently, a smaller atomic radius for Hafnium.
04

Conclude the reason for Hafnium breaking the general trend

As a result of the lanthanide contraction, Hafnium deviates from the general trend of increasing atomic radii while moving down a group in the periodic table. The weak shielding effect of the 4f electrons causes Hafnium's atomic radius to be smaller than expected, breaking the rule.

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