Question

In each of the following sets, which atom or ion has the smallest radius? a. \(\mathrm{H}, \mathrm{He}\) b. \(\mathrm{Cl}, \mathrm{In}, \mathrm{Se}\) c. element \(120,\) element \(119,\) element 116 d. \(\mathrm{Nb}, \mathrm{Zn}, \mathrm{Si}\) e. \(\mathrm{Na}^{-}, \mathrm{Na}, \mathrm{Na}^{+}\)

Short answer

The smallest atomic radii in each set are: a. \(\mathrm{He}\), b. \(\mathrm{Cl}\), c. element \(116\), d. \(\mathrm{Si}\), and e. \(\mathrm{Na}^{+}\).

Step-by-step solution

Identify the trend in the periodic table

Since hydrogen and helium are in the same period (Period 1), we know that the atomic size will decrease when moving across this period. In this case, helium will have a smaller atomic radius than hydrogen.

Determine the smallest radius

Since helium has the smallest atomic radius according to the periodic trend, the smallest radius in the set belongs to \(\mathrm{He}\). b. \(\mathrm{Cl}, \mathrm{In}, \mathrm{Se}\)

Identify the trend in the periodic table

Chlorine, indium, and selenium are all in different groups and periods. Therefore, we must compare their group and period trends. - Chlorine (Group 17, Period 3) - Indium (Group 13, Period 5) - Selenium (Group 16, Period 4) According to the trends, atomic size increases down a group (therefore, indium is larger than chlorine) and atomic size decreases across a period (selenium is smaller than indium).

Determine the smallest radius

Based on the trends, chlorine has the smallest atomic radius in the set. c. element \(120,\) element \(119,\) element \(116\)

Identify the trend in the periodic table

The elements are in the same period (period 7), so atomic size decreases across the period. Element 116 has the highest atomic number in the period, therefore, it has the smallest atomic radius. d. \(\mathrm{Nb}, \mathrm{Zn}, \mathrm{Si}\)

Identify the trend in the periodic table

Niobium, zinc, and silicon are in different periods and groups. Compare their group and period trends: - Niobium (Group 5, Period 5) - Zinc (Group 12, Period 4) - Silicon (Group 14, Period 3) Atomic size increases down a group and decreases across a period.

Determine the smallest radius

Based on the trends, silicon has the smallest atomic radius in the set. e. \(\mathrm{Na}^{-}, \mathrm{Na}, \mathrm{Na}^{+}\)

Determine the effect of charge on atomic radius

Cations (positive charges) have smaller atomic radii while anions (negative charges) have larger atomic radii. In this set of ions, the \(\mathrm{Na}^{-}\) ion has a negative charge, making its atomic radius larger, and the \(\mathrm{Na}^{+}\) ion has a positive charge, making its atomic radius smaller.

Determine the smallest radius

In the set, \(\mathrm{Na}^{+}\) has the smallest atomic radius due to its positive charge.

Key concepts

Periodic Trends

Understanding periodic trends is essential when analyzing the atomic radius of elements on the periodic table. These trends help predict how an element’s atomic properties will change based on its location on the table. Two major factors influence periodic trends:

• Moving across a period (left to right) typically decreases the atomic radius. The increased nuclear charge pulls electrons closer to the nucleus.
• Moving down a group (top to bottom) generally increases the atomic radius. This is due to the addition of electron shells, increasing the distance between the nucleus and the outer electrons.

As we go across a period, elements gain protons and their effective nuclear charge increases. This trend results in a smaller atomic size for elements situated further right in a period.
Conversely, as we go down a group, new electron shells outdistance the outermost electrons from the nucleus. Yet, despite a higher electron count, their atomic radius gets larger.

Atomic Size

Atomic size essentially describes the radius of an individual atom. It is a fundamental property taught in chemistry to understand how atoms interact. The atomic radius is the distance from the center of an atom's nucleus to the outermost electron shell.
Several factors influence atomic size:

• Effective nuclear charge: With stronger nuclear attraction, electrons are pulled closer, reducing atomic size.
• Electron shielding: More inner electron shells mean more shielding from nuclear force, expanding atomic size.
• Electron-electron repulsion: Additional electrons in the same shell repel each other, slightly increasing atomic radius.

As discussed in periodic trends, atomic size decreases across periods due to increased nuclear pulls but increases down groups owed to more substantial shielding effects.

Ionic Radius

Ionic radius refers to the size of an ion compared to the original atom. Ions can either be cations (positively charged) or anions (negatively charged), each affecting size differently.

• Cations are formed when atoms lose electrons. This process increases nuclear attraction on the remaining electrons, resulting in a smaller ionic radius compared to the neutral atom.
• Anions arise when atoms gain electrons. With extra electrons, increased electron-electron repulsion occurs, making the ionic radius larger than the neutral atom.

The process of gaining or losing electrons heavily influences the ionic radius, contrasting the atomic radius properties of the original elements. For example, a sodium ion \(\mathrm{Na}^{+}\) is smaller than its neutral state, whereas a chlorine ion \(\mathrm{Cl}^{-}\) is larger.

Periodic Table Groups and Periods

Each element on the periodic table occupies a specific location determined by its atomic number, electron configuration, and recurring chemical properties.
Groups refer to the vertical columns on the periodic table, while periods are the horizontal rows:

• Groups often contain elements with the same number of valence electrons, leading to similar chemical reactivity.
• Periods display a sequence of properties that do not consistently repeat. However, atomic size tends to decrease across periods and increase across groups.

For instance, when analyzing elements in the same group, the atomic radius generally increases as you move down the group, due to the addition of electron shells. Such organizing principles allow for the periodic table to be a powerful tool in predicting element behavior and properties.