Question

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

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

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.

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.

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.

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.

Key concepts

Atomic Radius

When studying the periodic table, a key trend often discussed is the atomic radius. Atomic radius refers to the size of an atom, typically measured from the nucleus to the outer boundary of the electrons. As you move down a group in the periodic table, the atomic radius tends to increase. Why, you might ask? Well, as you descend, each element has an additional electron shell compared to the one above it. This increase in the number of shells generally places the outermost electrons further from the nucleus, giving atoms a larger radius.
However, it is essential to note that other factors can influence this seemingly straightforward trend, causing exceptions. Some of these factors include electron shell shielding and nuclear charge. These will become important as we consider phenomena like the lanthanide contraction, which we'll touch upon next.

Lanthanide Contraction

Lanthanide contraction is an intriguing phenomenon that affects the periodic table, and it explains some unexpected patterns, such as the deviation in the atomic radius of hafnium. So what is lanthanide contraction? It occurs due to the poor shielding effect offered by 4f electrons. As you move through the lanthanides, from lanthanum to elements further along in the series like hafnium, additional electrons are added to the 4f subshell.
Despite the addition of these electrons, the 4f orbital does not efficiently shield the nuclear charge. This means that the effective nuclear charge experienced by the outer electrons actually increases. As a result, the outer electrons are pulled closer to the nucleus, leading to a smaller atomic radius than expected. Thus, although one might predict a continuous increase in atomic radius down a group, lanthanide contraction can cause an unexpected decrease, as observed with hafnium, which is smaller than its lanthanide precursor, lanthanum.

Effective Nuclear Charge

The concept of effective nuclear charge is crucial for understanding many periodic trends, including lanthanide contraction. Effective nuclear charge ( ext{Z}_{ ext{eff}} ) is the net positive charge experienced by valence electrons. It depends on the total number of protons in the nucleus and the screening effect of inner electrons.
As more protons are added to the nucleus moving across periods, ext{Z}_{ ext{eff}} increases. However, the shielding or blocking effect of internal electrons can vary. In the case of the lanthanides, the poorly shielding 4f electrons lead to each successive element experiencing a greater effective nuclear charge.
This increased pull from the protons pulls the electrons tighter to the nucleus. So, even though one would expect the atomic radius to increase, the increase in ext{Z}_{ ext{eff}} counteracts this, resulting in a smaller atomic radius for some elements like hafnium. This concept helps clarify why some elements break predictable patterns seen in the periodic table.