Question

Which of the following elements has an ionic radius that is larger than its atomic radius? 1\. \(\mathrm{Na}\) 2\. \(\mathrm{K}\) 3\. \(\mathrm{Mg}\) 4\. \(\mathrm{Cl}\)

Short answer

The element with an ionic radius larger than its atomic radius is 4. Chlorine (Cl). This is because chlorine gains an electron to form the Cl- ion, which results in an increased ionic radius compared to its atomic radius.

Step-by-step solution

Understanding atomic and ionic radii

Atomic radius is the distance from the nucleus to the outermost electron shell in an atom. Ionic radius, on the other hand, is the distance from the nucleus to the outermost electron shell in an ion (an atom with a charge due to gain or loss of electrons). When an atom loses an electron, it forms a positive ion (cation) and its size decreases because the effective nuclear charge (the net positive charge experienced by the electron) increases. When an atom gains an electron, it forms a negative ion (anion) and its size increases because the effective nuclear charge decreases. Now, let's analyze each element.

Sodium (Na)

Sodium is in Group 1 of the periodic table and has the electron configuration: \[1s^2 2s^2 2p^6 3s^1\] When sodium loses an electron, it forms the Na+ ion with the electron configuration: \[1s^2 2s^2 2p^6\] As a result, the ionic radius of sodium will be smaller than its atomic radius.

Potassium (K)

Potassium is in Group 1 of the periodic table and has the electron configuration: \[1s^2 2s^2 2p^6 3s^2 3p^6 4s^1\] When potassium loses an electron, it forms the K+ ion with the electron configuration: \[1s^2 2s^2 2p^6 3s^2 3p^6\] As a result, the ionic radius of potassium will be smaller than its atomic radius.

Magnesium (Mg)

Magnesium is in Group 2 of the periodic table and has the electron configuration: \[1s^2 2s^2 2p^6 3s^2\] When magnesium loses two electrons, it forms the Mg2+ ion with the electron configuration: \[1s^2 2s^2 2p^6\] As a result, the ionic radius of magnesium will be smaller than its atomic radius.

Chlorine (Cl)

Chlorine is in Group 17 of the periodic table and has the electron configuration: \[1s^2 2s^2 2p^6 3s^2 3p^5\] When chlorine gains an electron, it forms the Cl- ion with the electron configuration: \[1s^2 2s^2 2p^6 3s^2 3p^6\] As a result, the ionic radius of chlorine will be larger than its atomic radius. Based on the analysis, the correct answer is: 4. Chlorine (Cl)

Key concepts

Periodic Table Trends

Understanding the periodic table is crucial when we examine the properties of elements such as atomic and ionic radii. The periodic table is neatly organized into periods (horizontal rows) and groups (vertical columns), with each having specific trends.

Across a period, from left to right, atomic radii decrease due to the addition of protons in the nucleus. This results in a stronger effective nuclear charge, pulling electrons closer to the nucleus, making the atom smaller. Conversely, down a group, atomic radii increase because with each row, there is an additional electron shell which outweighs the increase in nuclear charge, causing the outermost electrons to be farther from the nucleus.

The ionic radius is also influenced by these position-based trends but is further impacted by the formation of cations and anions, which we will discuss in the next section.

Cation and Anion Formation

The formation of cations and anions alter an atom's size significantly. A cation is formed when an atom loses one or more electrons, resulting in a positive charge. As electrons are removed, electron-electron repulsion decreases, allowing the remaining electrons to be pulled closer by the nucleus. This process reduces the ionic radius compared to the atomic radius. For example, sodium (Na) when it loses an electron to become Na+, it drops an entire electron shell, significantly reducing its size.

In contrast, an anion is formed when an atom gains electrons, leading to a negative charge. The addition of electrons increases electron-electron repulsion, which can overcome the attraction of the additional electrons to the nucleus, leading to an increase in size. As we saw in the exercise, chlorine (Cl) gains an electron forming Cl-, which increases its ionic radius because its nuclear charge is relatively unchanged while adding an additional electron to the 3p subshell.

Effective Nuclear Charge

Effective nuclear charge (Z_eff) is a concept that helps explain the net positive charge felt by an electron in a multi-electron atom. The more effective the nuclear charge, the more tightly the electrons are held, and the smaller the radius of the atom or ion.

It is influenced by two main factors: the total number of protons in the nucleus, and the electron shielding or screening by the inner electron shells. As the inner electron shells increase, they shield the outer electrons from the full charge of the nucleus. However, as an atom transforms into a cation, it loses electrons, reducing the shielding effect and increasing the Z_eff. This increased Z_eff pulls the remaining electrons closer, hence reducing the ionic radius as compared to the atomic radius. Anions, on the other hand, experience a decrease in Z_eff relative to the number of protons, as the increase in electron count creates more repulsion and less effective pull from the nucleus, resulting in an increase in ionic radius.