Question

Zirconium and hafnium are the group \(4 \mathrm{~B}\) elements in the second and third transition series. The radii of these elements are virtually the same (Figure 23.20). Explain this similarity.

Short answer

The similarity in the radii of zirconium (Zr) and hafnium (Hf) can be explained by the shielding effect and the lanthanide contraction. Zr and Hf belong to Group 4 elements in the second and third transition series respectively. Though we expect an increase in atomic radius as we move down from Zr to Hf due to the addition of electron shells, the lanthanide contraction counteracts this effect. The poor shielding provided by the 4f electrons leads to an increased effective nuclear charge, resulting in a smaller atomic radius for Hf. Consequently, the atomic radii of Zr and Hf remain virtually the same.

Step-by-step solution

Identify the positions of Zirconium and Hafnium in the Periodic Table

Zirconium (Zr) and Hafnium (Hf) belong to Group 4 elements in the second and third transition series respectively. Zr has an atomic number of 40, while Hf has an atomic number of 72.

Define Atomic Radius

Atomic radius is defined as the distance from the center of an atom to the boundary of its electron cloud. It generally decreases across a period due to increased nuclear charge and increases down a group due to the addition of electron shells.

Discuss the Shielding Effect

The shielding effect is the reduction in effective nuclear charge felt by the outermost electrons due to the presence of inner (core) electrons. Inner electrons shield the outer electrons from the full attractive force of the nucleus, making it easier for outer electrons to be removed.

Explain Lanthanide Contraction

Lanthanide contraction is the gradual decrease in the atomic radii of elements as we move across the 4f series (from La to Lu). This is due to poor shielding of the 4f electrons, resulting in an increased effective nuclear charge and consequently, a smaller atomic radius.

Connect the Shielding Effect and Lanthanide Contraction to the Similar Radii of Zr and Hf

As we move down from Zr to Hf, the atomic number increases along with the addition of an electron shell (including the 4f series). However, due to the lanthanide contraction, the atomic radius of Hf does not increase as expected. The poor shielding provided by the 4f electrons results in an increased effective nuclear charge and a smaller atomic radius for Hf. This phenomenon counteracts the increase in atomic radius that should have occurred due to the additional electron shells. Thus, despite being in different periods, the atomic radii of Zr and Hf remain virtually the same.

Key concepts

Atomic Radius

Atomic radius is a fundamental property of atoms that directly influences the behavior and properties of elements. It is described as the measure from the center of the nucleus to the outermost stable orbit of the electrons. Understanding the atomic radius is crucial for predicting many chemical properties, such as bond lengths, ionization energy, and reactivity. A notable point to remember is that atomic radius tends to decrease across a period from left to right on the periodic table. This occurs because as additional protons are added to the nucleus, they increase the positive charge, pulling electrons closer and decreasing the radius. Conversely, when you move down a group, atomic radius increases since each successive element has an additional electron shell, adding greater distance between the outermost electrons and the nucleus.

For instance, in the given problem, Zirconium (Zr) has a smaller atomic radius compared to Hafnium (Hf) as predicted by its position in the periodic table. However, due to certain effects such as the lanthanide contraction, explained later, this expected difference in size does not occur.

Shielding Effect

The shielding effect explains the phenomenon where inner shell electrons repel outer shell electrons, effectively shielding them from the full magnetic pull of the positively charged nucleus. This effect plays a key role in determining atomic properties, as it affects how strongly the electrons are bound to the nucleus. In a simplified view, as the number of electron shells increases, the shielding effect becomes stronger, and the outermost electrons feel a weaker attraction to the nucleus. Therefore, electrons are more easily removed, and the atom displays different chemical properties.

However, the story gets more complex with the addition of electrons in the same shell, as in transition elements. These electrons do not contribute significantly to the shielding effect, leading to interesting trends in atomic sizes, which is especially apparent in the context of the lanthanide contraction.

Transition Elements

Transition elements are metals located in the middle of the periodic table and are characterized by the d subshell being partially filled with electrons. They are unique for their colorful compounds, variable oxidation states, and magnetic properties. An important aspect of transition metals is their similar atomic radii. Despite the addition of protons and electrons across a transition series, the atomic radii only change slightly. This is partly due to the poor shielding of d electrons and the increase in nuclear charge, which collectively pull the electron cloud inward. For this reason, elements such as Zirconium and Hafnium from different periods can have similar atomic sizes. This is strange because we generally expect the atomic radius to increase as we move down the group.

Periodic Table

The periodic table is a systematic arrangement of the chemical elements, organized by their atomic number, electron configuration, and recurring chemical properties. Elements are presented in order of increasing atomic number in rows called periods and columns called groups. As one moves from left to right across a period, elements become less metallic and more nonmetallic due to changes in atomic structure. The periodic table also helps in understanding the trends in atomic radius, electronegativity, ionization energy, and the shielding effect, which are all critical for predicting the behavior of elements and their compounds.

The relation between the periodic table and the lanthanide contraction is significant because the lanthanides, despite being a separate block, influence the properties of elements in the d block. This interaction is vital for understanding similarities in atomic radii among transition elements, overcoming the expectations based on their positions in the periodic table.