Question

The lanthanide contraction is responsible for the fact that (a) \(\mathrm{Zr}\) and Y have about the same radius (b) \(\mathrm{Zr}\) and \(\mathrm{Zn}\) have the same oxidation state (c) \(\mathrm{Zr}\) and Hf have about the same atomic radius (d) \(\mathrm{Zr}\) and \(\mathrm{Nb}\) have similar oxidation state

Short answer

(c) Zr and Hf have about the same atomic radius.

Step-by-step solution

Understand Lanthanide Contraction

Lanthanide contraction refers to the phenomenon where, instead of expanding as expected, the radius and volume of lanthanide elements decreases across the lanthanide series. This is due to poor shielding effect of f-electrons.

Examine Ionic Radii of Zr and Hf

Zirconium (Zr) and Hafnium (Hf) are in the same group of the periodic table, meaning they have similar electron configurations. Despite Hf having more protons and electrons than Zr, lanthanide contraction causes their atomic radii to be very similar.

Analyze Statement (c)

Statement (c) suggests Zr and Hf have about the same atomic radius. This is the direct result of lanthanide contraction, as explained in the previous steps. It accurately describes the phenomena.

Key concepts

Periodic Table

The periodic table organizes elements based on their atomic number, electron configurations, and recurring chemical properties. Elements are arranged in rows called periods, and columns known as groups or families. This arrangement helps in predicting the properties and behaviors of elements. For instance, elements in the same group often exhibit similar chemical behaviors due to their similar valence electron configurations.
Understanding the periodic table is crucial when studying concepts like the lanthanide contraction, which affects the elements in the lanthanide series of the periodic table. This is a set of 15 unique metal elements from Lanthanum to Lutetium, known for their contraction properties. The position of elements within the table can help explain certain periodic trends and anomalies, such as those seen with atomic radii and electron configurations.

Atomic Radii

Atomic radius is an essential concept in chemistry that describes the size of an atom. It is typically measured as the distance from the nucleus to the outermost electron shell. However, it can be affected by various factors, including the number of electron shells and the effective nuclear charge.
The lanthanide contraction is a phenomenon that particularly affects the atomic radii of elements within the lanthanide series. Normally, we expect atomic radii to increase as we move down a group due to the addition of electron shells. However, in the case of the lanthanides, the f-electrons added poorly shield the increased nuclear charge. As a result, the electrons are drawn closer to the nucleus, resulting in smaller radii.
This contraction impacts the transition metals like Zirconium (Zr) and Hafnium (Hf) that follow the lanthanides. Despite Hf having more protons and electrons, its atomic radius is nearly the same as Zr's, illustrating the effect of the lanthanide contraction. This anomaly is vital for understanding and predicting the behavior of transition metals.

Electron Configuration

Electron configuration is the distribution of electrons in an atom's orbitals and is crucial for understanding how elements will react chemically. It follows the principles of quantum mechanics and is typically noted in a format that denotes the number of electrons in each orbital shell.
In relation to the lanthanide contraction, understanding electron configuration gives insight into why the contraction occurs. For the lanthanides, the addition of electrons to the 4f orbitals leads to less effective shielding due to their complex shape and diffuse presence. This poor shielding by f-electrons allows the nucleus to pull the electron cloud closer, causing the contraction.
For elements like Zr and Hf, both of which are transition metals, their electron configurations influence their atomic radii and how they react chemically. Despite Hf having a more significant number of protons, the contraction caused by prior filling of the 4f orbitals results in a similar atomic radius to Zr. This unique occurrence demonstrates the interplay between electron configurations and atomic properties in the periodic table.