Question

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

Short answer

In each of the following sets, the atom or ion with the smallest radius is: a. He b. Cl c. Element 120 d. Si e. \(\mathrm{Na}^{+}\)

Step-by-step solution

Set(a) - H, He

In this set, we have Hydrogen (H) and Helium (He). Both elements are in the first period of the periodic table. Atomic radii decrease from left to right across a period due to increasing nuclear charge. Therefore, Helium (He) has the smallest atomic radius in this set.

Set(b) - Cl, In, Se

In this set, we have Chlorine (Cl), Indium (In), and Selenium (Se). Chlorine is in period 3 and group 17, Indium is in period 5 and group 13, and Selenium is in period 4 and group 16. Atomic radii decrease from left to right across a period and increase down a group due to increasing electron shielding. Among these elements, Chlorine (Cl) has the smallest atomic radius.

Set(c) - element 120, element 119, element 116

In this set, we have element 120, 119, and 116. As atomic numbers increase, atomic radii generally increase due to added electron shielding. However, the periodic trends play a more significant role in determining atomic radii. Element 116 is in group 16, element 119 is in group 1, and element 120 is in group 2. Atomic radii decrease from left to right across a period, so element 120 (group 2) will have the smallest atomic radius.

Set(d) - Nb, Zn, Si

In this set, we have Niobium (Nb), Zinc (Zn), and Silicon (Si). Niobium is in period 5 and group 5, Zinc is in period 4 and group 12, and Silicon is in period 3 and group 14. Atomic radii decrease from left to right across a period and increase down a group. Silicon (Si) is located farthest to the right and highest among these elements, so it has the smallest atomic radius in this set.

Set(e) - \(\mathrm{Na}^{-}, \mathrm{Na}, \mathrm{Na}^{+}\)

In this set, we have a sodium anion (Na⁻), a neutral sodium atom (Na), and a sodium cation (Na⁺). Comparing these species, the sodium cation (Na⁺) has lost an electron, resulting in a higher effective nuclear charge and a smaller atomic radius. Conversely, the sodium anion (Na⁻) has gained an electron, leading to increased electron shielding and a larger atomic radius. Thus, the sodium cation (Na⁺) has the smallest atomic radius in this set.

Key concepts

periodic table trends

The periodic table is organized in a way that displays periodic trends, which are patterns or tendencies in the properties of elements. One important trend is the variation in atomic radii. Moving from left to right across a period, atomic radii decrease. This happens because the effective nuclear charge increases as the number of protons in the nucleus increases, pulling electrons closer to the nucleus.
Additionally, going down a group, atomic radii increase. This is due to additional electron shells that are added as elements move to higher periods. In essence, the number of electron shells (or energy levels) increases, causing electrons to be further from the nucleus.
Key points of these trends include:

• Atomic radii decrease across a period due to increased nuclear charge without additional shielding.
• Atomic radii increase down a group as more electron shells are added.

This understanding is crucial for predicting the relative sizes of atoms and ions based on their positions in the periodic table.

cation and anion size

When atoms gain or lose electrons to become ions, their sizes change. Cations are positively charged ions formed when an atom loses one or more electrons. This loss leads to a reduction in atomic radius due to increased effective nuclear charge per electron. Essentially, there are fewer electrons to shield one another, allowing the nucleus to pull them closer.
Conversely, anions are negatively charged ions formed when an atom gains electrons. The addition of extra electrons increases electron-electron repulsion and can lead to larger atomic radii. The increased electron shielding effect counteracts the nuclear pull, resulting in a greater atomic radius.
It's important to remember:

• Cations are smaller than their neutral atoms because they have fewer electrons, resulting in decreased shielding.
• Anions are larger than their neutral atoms because they have additional electrons, leading to increased shielding.

Knowing these differences helps predict the size of ions compared to their neutral atoms and among different ions.

electron shielding

Electron shielding, also known as screening, occurs when inner shell electrons block the attraction between the nucleus and the outer shell electrons. This influences the effective nuclear charge felt by the outermost electrons.
As electrons are added to atoms moving down a group in the periodic table, they fill inner energy levels, which shield the outer electrons from the full effect of the positive charge of the nucleus. This results in larger atomic radii since the outermost electrons experience a weaker effective nuclear charge.
Key points about electron shielding include:

• Inner electrons partially block the nuclear charge, reducing the force felt by valence electrons.
• This effect increases with additional energy levels as you move down a group, contributing to larger atomic sizes.

Understanding electron shielding is important for predicting how atomic size changes with the addition of electron shells.

effective nuclear charge

The effective nuclear charge ( Z_{eff} ) is the net positive charge experienced by valence electrons. It determines how strongly outer electrons are held to the nucleus. The actual nuclear charge is reduced by electron shielding from inner shell electrons.
The effective nuclear charge increases across a period from left to right. This is because the number of protons (nuclear charge) increases, but the principal energy level remains constant, leading to less shielding. Hence, electrons are pulled closer, causing a decrease in atomic size.
When considering Z_{eff}:

• Across a period, Z_{eff} increases as additional protons attract electrons more strongly.
• The increase in Z_{eff} across a period contributes to a decrease in atomic and ionic sizes.

Effective nuclear charge is a crucial factor in understanding periodic trends and differences in atomic and ionic sizes.