Problem 88 - Chemistry The Central Science In Si Units

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 Zr to Hf are the same. Suggest an explanation for this effect. $$ \begin{aligned} &\text { Atomic Radii (pm) }\\\ &\begin{array}{cccc} \hline \text { Sc } & 170 & \text { Ti } & 160 \\ \text { Y } & 190 & \text { Zr } & 175 \\ \text { La } & 207 & \text { Hf } & 175 \\ \hline \end{array} \end{aligned} $$

Step-by-Step Solution

Answer

The increase from Y to La is due to added electron shells; the constant radii from Zr to Hf result from lanthanide contraction.

Step 1: Understand Periodic Trends

Atomic radius generally decreases across a period from left to right in the periodic table due to the increasing positive charge of the nucleus pulling the electron cloud closer.

Step 2: Examine Y to La Transition

When moving from Y (Yttrium) to La (Lanthanum), we move into the lanthanide series. Lanthanides have an additional electron shell compared to their preceding elements, leading to a larger atomic radius due to the additional layer of electrons.

Step 3: Examine Zr to Hf Transition

Moving from Zr (Zirconium) to Hf (Hafnium), both elements hold the same electron configuration beyond filled shells and have similar shielding effects. Hafnium's additional protons increase the nuclear charge, but the f-electron subshell does not shield these effectively, and thus the radius remains similar.

Step 4: Explain the Lanthanide Contraction

The observation that the radii of Hf remain similar compared with Zr is a result of the lanthanide contraction. This occurs because of the poor shielding provided by 4f electrons in lanthanides, allowing added protons in subsequent elements to pull the electrons closer.

Key Concepts

Atomic Radius

The atomic radius refers to the size of an atom, typically measured from the nucleus to the outer boundary of the surrounding cloud of electrons. It is an essential indicator of the chemical properties of an element. As you move across a period from left to right in the periodic table, the atomic radius generally decreases. This reduction is due to the increased positive charge of the nucleus, which attracts the electron cloud more strongly and pulls it closer to the core. Conversely, as you move down a group, the atomic radius increases because additional electron shells are added, outweighing the nuclear attraction due to added protons.

• The nucleus gets more positively charged as you move right.
• Electrons are added to the same shell in a period, increasing nuclear pull.
• While moving down, new shells are added, increasing the radius.

Understanding how atomic radius varies is crucial when predicting how elements react and form bonds, impacting their involvement in forming various compounds.

Lanthanide Contraction

Lanthanide contraction is a unique phenomenon observed in the elements of the period following the lanthanides. When analyzing elements such as Zirconium (Zr) and Hafnium (Hf), despite being in different groups, their atomic radii are quite similar. This surprise is due to the poor shielding effect of the 4f orbitals present in lanthanides preceding Hafnium. Even though these orbitals are deeply buried, they don't shield the nuclear charge effectively. This means that protons added as you move across the lanthanide series draw electrons closer, reducing atomic size despite the increase in shell number.

• 4f orbitals have poor shielding ability.
• Protons draw electrons closer as they add up.
• Leads to small size variation in elements after lanthanides.

This factor plays a significant role in explaining why Hafnium and Zirconium have nearly identical atomic sizes even though Hafnium has more protons. This subtlety impacts chemistry significantly, influencing element reactivity and physical characteristics.

Electron Configuration

Electron configuration describes the distribution of electrons in an atom's orbitals. It follows the Aufbau principle, filling shells and subshells starting from the lowest energy level ascending to higher levels. This order is crucial in understanding the chemical properties and reactivity of elements. As you transition from Y (Yttrium) to La (Lanthanum), a new electron shell begins to fill, causing an increase in atomic radius. This is because the added electrons occupy a new, more distant shell, increasing the atom's size.

• Predicts how electrons are arranged in atoms.
• Determines chemical reactivity and bonding patterns.
• Aufbau principle guides filling of electrons in orbitals.

On the other hand, when moving from Zr to Hf, despite an additional electron in a new f subshell, due to lanthanide contraction, the radius does not increase as expected. This is a perfect example of how intricate and impactful electron configuration can be in understanding elemental properties.