Question

Predict which element in the pair has the larger atomic radius. (a) Cu or Ag (b) \(\mathrm{T} \mathrm{i}\) or \(\mathrm{Cr}\) (c) W or \(\mathrm{Hg}\)

Short answer

(a) Ag, (b) Ti, (c) W

Step-by-step solution

Understanding Atomic Radius

The atomic radius of an element is an indication of the size of its atoms, usually the mean or typical distance from the nucleus to the boundary of the surrounding cloud of electrons. Typically, atomic radius increases as, in the periodic table, moving down a group and decreases when moving from left to right across a period.

Compare Atomic Radius: Cu vs Ag

Copper (Cu) and Silver (Ag) are both in Group 11 of the periodic table, with Silver located below Copper in the same group. As we move down a group in the periodic table, the atomic radius generally increases due to the addition of more electron shells. Therefore, Ag typically has a larger atomic radius than Cu.

Compare Atomic Radius: Ti vs Cr

Titanium (Ti) and Chromium (Cr) are in the same period (Period 4) of the periodic table, with Ti being to the left of Cr. Moving across a period from left to right, the atomic radius generally decreases because the effective nuclear charge increases, pulling the electron cloud closer to the nucleus. Therefore, Ti has a larger atomic radius than Cr.

Compare Atomic Radius: W vs Hg

Tungsten (W) and Mercury (Hg) are both in Period 6, with Hg further to the right than W and in a different group. While it typically holds that atomic radii decrease across a period, the effects of relativistic contraction in Hg's electron cloud make its radius smaller than expected for its position. Therefore, W has a larger atomic radius than Hg.

Key concepts

Periodic Table Trends

Periodic table trends are essential to understanding the behavior of elements and their properties, especially the atomic radius. The atomic radius is crucial as it indicates the size of an atom by measuring the distance from the nucleus to the outermost electrons.
When observing trends across the periodic table:

• Atomic radius decreases across a period (from left to right). This is because as you move to the right, elements have more protons which increases the effective nuclear charge, pulling electrons closer to the nucleus.
• Atomic radius increases down a group (top to bottom). This is due to the addition of electron shells, which are further away from the nucleus, effectively increasing the size of the atoms.

Understanding these trends allows us to predict and compare the atomic radius of elements based on their positions in the periodic table.

Group and Period Trends

The periodic table is organized into groups and periods, where each arrangement reveals trends in elemental properties. Groups consist of vertical columns, and elements within a group typically share similar characteristics due to having the same number of valence electrons.
In terms of atomic radius:

• Within a group, as you move down, each element has additional electron shells. These shells increase the distance from the nucleus to the outermost electron cloud, hence increasing the atomic radius.
• Periods are horizontal rows. Within a period, moving from left to right, elements gain protons, increasing the effective nuclear charge. This increased charge pulls electrons closer to the nucleus, resulting in a decrease in atomic radius.

By understanding these trends, we can predict that elements at the bottom of a group exhibit larger atomic radii than those at the top, while those on the left of a period have larger atomic radii than those on the right.

Electron Shells

Electron shells play a significant role in determining the size of an atom or its atomic radius. These shells indicate the levels where electrons are located around the nucleus.
When moving down a group in the periodic table:

• Each subsequent element gains an additional electron shell compared to the element above it. This increase in the number of electron shells results in a greater atomic radius.
• These shells are arranged in increasing energy levels further from the nucleus, spreading the electron cloud and enhancing the atomic size.

Thus, more electron shells generally mean a larger atomic radius. This explains why atoms get larger as you go down a group, because each element has more electron layers than the one above it.

Effective Nuclear Charge

Effective nuclear charge (often abbreviated as \(Z_{eff}\)) is a measure of the positive charge felt by the outermost electrons in an atom. It can greatly influence the atomic radius and various other chemical properties of elements.

• As you move across a period from left to right, the number of protons (and hence positive charge) in the nucleus increases. This causes a greater pull on the electrons surrounding the nucleus.
• This stronger pull brings the electron cloud closer, resulting in a decrease in atomic radius. The electrons feel a stronger attraction due to the high effective nuclear charge.
• However, moving down a group, the effective nuclear charge remains relatively constant due to the shielding effect, where inner electrons block the outer electrons from feeling the full charge of the nucleus.

The concept of effective nuclear charge not only helps in understanding the size of atoms but also provides insights into other properties like ionization energy and electronegativity.