Question

The largest of the following is (a) an Ar atom; (b) a \(\mathrm{K}^{+}\) ion; \((c) a C a^{2+}\) ion; \((d) a C l^{-}\) ion.

Short answer

\(Cl^{-}\) ion is the largest among the given atoms/ions.

Step-by-step solution

Analysis of Ar atom

Argon (Ar) is in Period 3 of the periodic table. It has 3 energy levels occupied by electrons. Since it is a neutral atom, there are no changes in the nuclear charge due to the loss or gain of electrons.

Analysis of \(K^{+}\) ion

Potassium (K) is also in Period 4 of the periodic table. However, the \(K^{+}\) ion indicates that it has lost one electron, which also means it has lost an energy level. Therefore, \(K^{+}\) has only 3 energy levels occupied by electrons. Additionally, with the loss of an electron, the nuclear charge increases which pulls the electrons closer to the nucleus, reducing the size of the ion.

Analysis of \(Ca^{2+}\) ion

Calcium (Ca) is in Period 4 of the periodic table. The \(Ca^{2+}\) ion means that Calcium has lost 2 electrons and therefore lost an energy level. Hence, \(Ca^{2+}\) has 3 energy levels occupied by electrons. Moreover, the increase in nuclear charge due to the loss of electrons decreases the size of the ion.

Analysis of \(Cl^{-}\) ion

Chlorine (Cl) is in Period 3 of the periodic table. The gaining of an electron to form \(Cl^{-}\) doesn't add an energy level. Thus, \(Cl^{-}\) has 3 energy levels. However, the nuclear charge decreases with the addition of an electron, increasing the size of the ion.

Comparison and conclusion

From the analysis of the 4 atoms/ions, we see that all have 3 energy levels occupied by electrons. However, the \(K^{+}\) and \(Ca^{2+}\) ions have an increased nuclear charge, which makes them smaller than Ar and \(Cl^{-}\). Comparing Ar and \(Cl^{-}\), the decreased nuclear charge of \(Cl^{-}\) makes it larger than Ar. Hence, among the given atoms/ions, \(Cl^{-}\) has the largest size.

Key concepts

Energy Levels

Energy levels, also known as electron shells, refer to the fixed distances from the nucleus of the atom where electrons may exist. Each level can hold a specific number of electrons and is defined by the principal quantum number, denoted as \(n\). For example, elements in Period 3 of the periodic table, like Argon (Ar), have electrons in the first, second, and third energy levels.

• Energy levels determine where electrons reside about the nucleus.
• When an atom loses or gains electrons, the number of occupied energy levels can change.

Potassium (K), in its neutral state, has four energy levels filled, but as a \(K^{+}\) ion, it loses an electron in the outermost level, resulting in only three occupied energy levels. Likewise, Calcium (Ca) becomes \(Ca^{2+}\) by losing two electrons and ultimately sheds an entire outer energy level. Understanding these shifts is critical for explaining atomic radii changes as ions form.

Nuclear Charge

The nuclear charge, essentially the total positive charge of the nucleus, is due to protons. It influences the force exerted on electrons, drawing them closer to the nucleus. When an electron is lost or gained, the nuclear charge experienced by the remaining electrons changes.

• Positive nuclear charge tends to pull electrons inward, thereby affecting the size of the ion or atom.
• When electrons are lost, as in \(K^{+}\) or \(Ca^{2+}\), the effective nuclear charge increases.

This increase in effective nuclear charge arises because the proton-to-electron ratio has increased, enhancing the nucleus's ability to attract the remaining electrons inward. Conversely, when an electron is gained, as in the formation of \(Cl^{-}\), the effective nuclear charge perceived by each electron decreases, allowing them to spread slightly farther apart, increasing the atomic size.

Periodic Table

The periodic table is a comprehensive map of chemical elements arranged by increasing atomic number. Its layout reveals patterns in element properties, notably electron configurations and atomic sizes.

• Elements are organized into periods (rows) and groups (columns).
• Moving across a period from left to right, additional valence electrons and protons lead to a stronger effective nuclear charge.

In the context of the exercise, noticing where each element or ion falls on the periodic chart helps predict its behavior. Argon (Ar), Potassium (K), and Calcium (Ca) all belong to Period 3 or 4 and, therefore, utilize similar energy levels, whereas Chlorine (Cl) and its negative ion form \(Cl^{-}\) contribute to understanding size variations based on their placement within these periods.

Ionic Size

The size of an ion compared to its neutral atom form is largely dictated by its electron configuration changes and effective nuclear charge. Ionic size often varies based on whether an atom loses or gains electrons.

• Loss of electrons (forming cations) typically results in a smaller ion due to decreased electron-electron repulsion and increased effective nuclear pull.
• Gaining electrons (forming anions) usually leads to a larger ion due to increased electron-electron repulsion and a spread-out electron cloud.

When analyzing the \(Cl^{-}\) ion, its larger size compared to Ar, \(K^{+}\), or \(Ca^{2+}\) is due to additional electron repulsion and reduced nuclear charge effect. Conversely, \(K^{+}\) and \(Ca^{2+}\) ions shrink due to the stronger inward pull from their unchanged protons acting upon a diminished electron cloud, thus decreasing their size relative to their neutral counterparts.