Question

Note from the following table that the increase in atomic radius in moving from \(\mathrm{Zr}\) to \(\mathrm{Hf}\) is smaller than in moving from \(\mathrm{Y}\) to La. Suggest an explanation for this effect. \begin{tabular}{llll} \hline \multicolumn{3}{l} { Atomic Radii \((\AA)\)} \\ \hline Sc & 1.44 & \(\mathrm{Ti}\) & 1.36 \\ \(\mathrm{Y}\) & 1.62 & \(\mathrm{Zr}\) & 1.48 \\ \(\mathrm{La}\) & 1.69 & \(\mathrm{Hf}\) & 1.50 \end{tabular}

Short answer

The smaller increase in atomic radius from Zr to Hf compared to Y to La is primarily due to the lanthanide contraction effect. The 5d electrons in Hf experience a stronger attraction to the nucleus because of the lesser shielding effect of the 4f electrons, resulting in a smaller atomic radius for Hf compared to La.

Step-by-step solution

Electron Configuration

We have to first consider the electron configurations of the elements mentioned in the question. As we go across the periodic table from left to right, we fill up orbitals from 4d to 5f to 6s. Let's write down the electron configurations for Y, Zr, La, and Hf. - Yttrium (Y): \[1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^1\](Z = 39) - Zirconium (Zr): \[ 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^2\](Z = 40) - Lanthanum (La): \[ 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^1 5p^6 6s^2\] (Z = 57) - Hafnium (Hf): \[1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^6 5s^2 4d^1 5p^6 4f^{14} 5d^2 6s^2\](Z = 72) From the electron configurations, we can see that going from Y to Zr involves adding an electron in the 4d orbital while going from La to Hf includes an electron filling up the 5d orbital.

Effective Nuclear Charge

Now let's consider the effective nuclear charge (Z_eff). As the number of protons increases while moving across the periodic table, this will increase the positive charge within the nucleus. Meanwhile, the shielding effect of core electrons remains almost constant. Hence, the net positive charge experienced by the valence electrons will increase. This would result in a greater attraction between the nucleus and valence electrons, thereby decreasing the atomic radii.

Lanthenide Contraction Effect

For elements in the 4f block (f-block elements), an important effect called "lanthanide contraction" needs to be considered. The lanthanide contraction refers to the gradual filling of the 4f orbitals, which have a lower shielding effect as compared to the other orbitals (s, p, and d orbitals). Since Hf is located right after the lanthanide series, the 5d electrons of Hf experience a stronger attraction to the nucleus due to the lesser shielding effect of 4f electrons. This leads to a decrease in atomic radii.

Conclusion

In conclusion, the atomic radii increase when moving from Y to La and Zr to Hf. The increase in atomic radii from Y to La is larger than the increase from Zr to Hf due to the lanthanide contraction effect, which causes the 5d electrons in Hf to be more strongly attracted to the nucleus due to the lesser shielding effect of the 4f electrons. This leads to a smaller atomic radius for Hf as compared to La.

Key concepts

Atomic Radii

Understanding atomic radii is crucial when comparing different elements on the periodic table. Atomic radii refer to the size of an atom from its nucleus to the outer boundaries of its electron cloud. Generally, atomic radii decrease from left to right across a period due to an increase in the effective nuclear charge, which pulls electrons closer to the nucleus, reducing the size of the atom.

However, exceptions to this trend occur, as seen in the exercise, where the difference in atomic radii between Yttrium (Y) and Lanthanum (La) is more pronounced than that between Zirconium (Zr) and Hafnium (Hf). This phenomenon can be attributed to factors such as the 'lanthanide contraction', which will be explored further in relation to other core concepts.

Electron Configuration

The electron configuration of an element describes the distribution of electrons in its atomic orbitals. This configuration not only determines the chemical properties of an element but also affects its atomic radii. When we examine elements like Y, Zr, La, and Hf, we observe a filling of orbitals from 4d onwards.

The order in which these orbitals are filled has implications for atomic size. For instance, the 4f orbitals in the lanthanides—poorly shielding the nuclear charge—result in a smaller atomic radius for Hafnium when compared to Lanthanum. This can be surprising since both follow a filling of d orbitals, yet they demonstrate different trends in atomic size due to their electron configurations.

Effective Nuclear Charge

Effective nuclear charge (Z_eff) is a term that refers to the net positive charge experienced by an electron in a multi-electron atom. The concept explains why valence electrons are attracted more strongly to the nucleus as protons are added. This increased attraction tends to shrink the atom, making the effective nuclear charge a key player in understanding periodic table trends, especially when contrasting atomic radii among different elements.

In the case of the increase in radius from Y to La versus Zr to Hf, Z_eff is also responsible for the differing extents of increase. The increased Z_eff in Hf due to poor shielding by 4f electrons results in a smaller radius increment when compared with that between Y and La.

Periodic Table Trends

Analyzing trends in the periodic table is fundamental to predicting and explaining the chemical and physical properties of elements. One such trend is the variation of atomic radii. Typically, atomic size decreases across a period and increases down a group. These trends highlight the balance between the attraction of electrons towards the nucleus and the repulsion between electrons in different shells.

The puzzle presented in the exercise underscores an irregularity in these trends, which can be deciphered by considering additional concepts like the 'lanthanide contraction' alongside more familiar trends such as the increase of Z_eff across a period. This adds depth to our understanding of the periodic behavior of elements.

Shielding Effect

The shielding effect relates to the reduction in the effective nuclear charge on the outermost electrons due to repulsion from electrons in inner orbitals. In a nutshell, core electrons can 'shield' valence electrons from the full charge of the nucleus. The effectiveness of this shielding varies with electron configurations; for instance, d and f orbitals do not shield as effectively as s and p orbitals. As a result, the inner 4f electrons in the lanthanides do not offer substantial shielding, leading to the 'lanthanide contraction effect.'

This shielding effect, or the lack thereof, in lanthanide elements explains the smaller atomic radius exhibited by Hafnium compared to expected trends, as seen in the textbook exercise. Understanding the shielding effect helps to clarify why the lanthanide contraction occurs and its impact on periodic trends.