Question

Which should be larger, the potassium atom, \(\mathrm{K}\), or the potassium ion, \(\mathrm{K}^{+}\)?

Short answer

The potassium atom (K) is larger than the potassium ion (K\(^+\)).

Step-by-step solution

Understanding Atomic and Ionic Sizes

Atoms and ions have different sizes due to changes in the electron cloud when they form cations or anions. When an atom loses an electron to form a cation, the remaining electrons experience a greater effective nuclear charge, pulling them closer to the nucleus.

Identify the Change in Potassium Atom

A neutral potassium atom, \( ext{K} \), has 19 electrons. Its electron configuration is \( [ ext{Ar} ] 4s^1 \). It has a relatively large atomic radius due to the presence of a single valence electron in the 4s orbital, which is far from the nucleus.

Forming the Potassium Ion

When potassium forms a \( ext{K}^+ \) ion, it loses its one valence electron from the 4s orbital. This leaves the electronic configuration of \( [ ext{Ar} ] \), reducing the number of electron shells and causing the remaining electrons to be held more closely by the nucleus.

Comparison of Sizes

The loss of the outermost electron shell in \( ext{K}^+ \) means it has fewer electron shells compared to the neutral \( ext{K} \). This results in a smaller radius for the potassium ion compared to the potassium atom.

Key concepts

Electron Configuration

Electron configuration is the arrangement of electrons in an atom or ion. It can be thought of as the map of where all of an atom's electrons "live" or are "located" at various energy levels or "shells." In its ground state, potassium has the electron configuration of \([\text{Ar}]\ 4s^1\). This means potassium has a total of 19 electrons, with the first 18 filling up lower energy levels (matching the electron configuration of argon, \([\text{Ar}]\)), and the 19th electron residing in one 4s orbital at a higher energy level.

• The position of electrons in an atom determines its chemical properties.
• The outermost electrons, or valence electrons, are crucial since they are involved in bonding.
• Losing, gaining, or sharing electrons can change an atom into an ion, altering its electron configuration.

In the case of potassium, losing its 4s electron forms \(\text{K}^+\), resulting in the configuration \([\text{Ar}]\). This significant change explains the shift in size when forming ions.

Cations vs Anions

Atoms become ions when they lose or gain electrons. The type of ion formed can either be a cation or an anion:

• Cations are positive ions formed by the loss of one or more electrons. This often occurs with metals. Potassium, for example, loses one electron to become \(\text{K}^+\).
• Anions are negative ions formed by the gain of electrons. Nonmetals commonly form anions.

When an atom, like potassium, becomes a cation, its radius decreases. This is because:

• The loss of electrons results in fewer electron shells, making the ion smaller.
• The remaining electrons experience a stronger attraction towards the nucleus since there are more protons than electrons. This pulls the electron cloud closer.

This concept explains why \(\text{K}^+\) is smaller than a neutral potassium atom \(\text{K}\).

Effective Nuclear Charge

The effective nuclear charge \( (Z_{\text{eff}}) \) is the net positive charge experienced by valence electrons. It is essentially how much "pull" the electron feels from the nucleus, after accounting for shielding by inner-shell electrons The effective nuclear charge explains a lot about an atom's behavior:

• More protons in the nucleus increase the positive pull experienced by electrons, but inner electrons can shield outer electrons from this full positive force.
• Even after losing an electron (as in potassium forming \(\text{K}^+\)), the remaining electrons experience an increased \(Z_{\text{eff}}\), pulling them closer to the nucleus.

In other words, the core electrons act as a barrier between the nucleus and the valence electrons. This concept helps us understand why the ionic radius of \(\text{K}^+\) is smaller than that of \(\text{K}\), as the remaining electrons are more tightly held to the nucleus due to the increased effective nuclear charge.