Question

Note from the following table that there is a significant increase in atomic radius upon moving from \(\mathrm{Y}\) to La whereas the radii of \(\mathrm{Zr}\) to \(\mathrm{Hf}\) are the same. Suggest an explanation for this effect. $$ \begin{array}{llll} \hline & {\text { Atomic Radii (Å) }} \\ \hline \mathrm{Sc} & 1.70 & \mathrm{Ti} & 1.60 \\ \mathrm{Y} & 1.90 & \mathrm{Zr} & 1.75 \\ \mathrm{La} & 2.07 & \text { Hf } & 1.75 \\ \hline \end{array} $$

Short answer

In conclusion, the significant increase in atomic radius from Y to La can be explained by the poor shielding effect provided by the f-electrons, which causes the valence electrons to be pulled closer to the nucleus, leading to a larger atomic radius. On the other hand, the atomic radii of Zr and Hf remain the same as they have comparable electron configurations, and d-electrons provide better shielding effects as compared to the f-electrons.

Step-by-step solution

Identify the electron configurations

In order to understand the pattern in atomic radii, first, let's write the electron configurations of Y, La, Zr, and Hf. Y atomic number: 39 Y electron configuration: \([Kr] 5s^2 4d^1\) La atomic number: 57 La electron configuration: \([Xe] 6s^2 5d^1 4f^0\) Zr atomic number: 40 Zr electron configuration: \([Kr] 5s^2 4d^2\) Hf atomic number: 72 Hf electron configuration: \([Xe] 6s^2 4f^{14} 5d^2\)

Notice the f-orbital contribution

Next, compare the electron configurations between these elements. You will see that Y to La transition introduces the f-orbital, specifically a 4f^0 configuration for La, while Zr and Hf have similar electron configurations with filled f-orbitals. Notice that the f-orbitals are not completely filled in the case of La and they are completely filled (4f^14) in the case of Hf.

Linked effects of transition elements and f-orbitals shielding on atomic radii

As we move from Y to La, electrons start to fill up the f-orbitals. This results in a poor shielding effect, as f-electrons do not shield valence electrons very effectively. The unavailability of f-electrons to provide effective shielding increases the nuclear charge experienced by valence electrons, making them closer to the nucleus. This results in a larger atomic radius. In the case of Zr and Hf, they are both transition elements, with d-electrons dominating their atomic radii. Since d-electrons are better at providing shielding effects than f-electrons, there is no significant change in the shielding and hence, in their atomic radii while moving from Zr to Hf.

Conclude the explanation

In conclusion, the significant increase in atomic radius from Y to La can be explained by the poor shielding effect provided by the f-electrons, which causes the valence electrons to be pulled closer to the nucleus, leading to a larger atomic radius. On the other hand, the atomic radii of Zr and Hf remain the same as they have comparable electron configurations, and d-electrons provide better shielding effects as compared to the f-electrons.

Key concepts

Electron Configuration

Understanding electron configuration is crucial for explaining atomic behaviors. Each element's position in the periodic table helps determine its electron configuration. This configuration refers to the distribution of electrons in an atom’s orbitals, usually depicted starting from the lowest energy level upwards.
For instance, consider the electron configuration for yttrium (Y):

• Y atomic number: 39
• Y electron configuration: \([Kr] 5s^2 4d^1\)

When moving to lanthanum (La), the electron configuration is:

• La atomic number: 57
• La electron configuration: \([Xe] 6s^2 5d^1 4f^0\)

With zirconium (Zr) and hafnium (Hf), their configurations are:

• Zr atomic number: 40 <: 45d^2
• Hf atomic number: 72 <: 45d^2 4f^{14}

By examining these configurations, we see the transition from Y to La includes the introduction of f-orbitals. This introduction helps explain variations in atomic radius due to changes in electron shell occupation.

F-orbitals

F-orbitals play a critical role in understanding the unique behavior of certain elements, particularly when explaining phenomena such as changes in atomic radii.
F-orbitals are part of the atom’s more complex sublevel structures, positioned higher than d-orbitals in terms of energy. They can hold up to 14 electrons, and their involvement often results in intriguing changes in atomic properties.
In La, although the 4f orbital is EMPTY, the existence becomes evident as it pulls electrons closer to the nucleus, diminishing atomic radius. When moving to Hf, the 4f orbitals become fully filled with electrons \(4f^{14}\), holding and further stabilizing atomic structure.
Thus, f-orbitals contribute significantly to poor shielding effects, highlighting their significant impact on electron interactions, energy levels, and change management within an element.

Shielding Effect

The shielding effect is essential to the understanding of atomic size differences. This effect refers to how electrons in inner shells can reduce the full nuclear charge impact felt by valence electrons.
The presence of additional electrons in these inner shells "shields" outer electrons, often mitigating the nucleus's pull on them. However, f-orbitals are notorious for their poor shielding ability.
In elements like La, where f-electrons are first introduced, they hardly shield the outer shells, allowing valence electrons to feel more nuclear charge. This results in valence electrons moving closer, thus reducing atomic size as seen between Y and La.

• Effective shielding observed with d-electrons.
• Minimal shielding by f-electrons compared to d-electrons.

In contrast, between Zr and Hf, d-electrons offer a better shielding effect, leading to no notable change in atomic radii. Understanding this concept is key to grasping differences in physical properties within the periodic table.