Question

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

Short answer

The argon atom is larger than the potassium ion.

Step-by-step solution

Understand Ion and Neutral Atom Sizes

To compare the sizes of a potassium ion (\( \text{K}^+\) ) and an argon atom (Ar), it's important to know that ions and neutral atoms have different sizes. An ion has lost or gained electrons, which can affect its size.

Review Electron Configuration of Neutral Atoms

Neutral potassium (\( \text{K} \) ) has an electron configuration of [Ar] 4s^1, and neutral argon (\( \text{Ar} \) ) has [Ne] 3s^2 3p^6. Argon has a stable, filled outer shell with 18 electrons.

Compare Potassium Ion and Argon Size

The potassium ion (\( \text{K}^+ \) ) is formed by losing one electron, making its electron configuration the same as argon, [Ar]. However, due to the loss of an electron, the \( \text{K}^+ \) ion has less electron-electron repulsion and a smaller size than the neutral argon atom.

Key concepts

Electron Configuration

Electron configuration is the arrangement of electrons within an atom or ion. It's like the blueprint of where an atom's electrons hang out. Understanding electron configurations helps us make sense of an atom's behavior and characteristics. For example, neutral potassium (K) has the electron configuration of

• 1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹

Whereas neutral argon (Ar), a noble gas, has a more stable electron configuration of

• [Ne] 3s² 3p⁶

This means argon has a complete outer shell, which is why it is very stable and doesn't easily react with other elements.
Electron configurations are key to understanding an atom's reactivity, stability, and size.

Potassium Ion

When a neutral potassium atom loses an electron, it becomes a potassium ion (\[\text{K}^+\]). This ion has gained a positive charge due to the loss of a single electron from its outermost shell. The original electron configuration of neutral potassium is

• [Ar] 4s¹

After losing the electron, the ion's configuration becomes

• [Ar]

This means that the potassium ion now has the same electron configuration as argon. However, the fact that it lost an electron makes the \[\text{K}^+\] ion physically smaller than the neutral argon atom. This is primarily due to the reduced electron-electron repulsion.

Argon Atom

The argon atom is a noble gas with a stable electron configuration. It contains 18 electrons arranged as

• [Ne] 3s² 3p⁶

which completes its outer electron shell. Argon's stability comes from having a full set of valence electrons, making it unreactive under normal conditions.
This complete valence shell signifies a lack of desire to gain or lose electrons, which is a hallmark of noble gases. Because of this stable configuration, the argon atom is larger than an equivalent ion such as \(\text{K}^+\). Although both have the same electron configuration, argon maintains greater size because of the intact neutral charge and the balanced electron-electron repulsion.

Electron-Electron Repulsion

Electron-electron repulsion is an important factor in determining the size of an atom or ion. Electrons are negatively charged and naturally repel each other, much like a group of people trying to maximize personal space in a crowded room. This repulsion affects the overall atomic radius.
When a neutral atom loses an electron, like in the case of potassium losing an electron to become \(\text{K}^+\), the reduced electron count results in less repulsion among the remaining electrons. This causes the ion to shrink in size compared to the original atom.
In neutral atoms like argon, even with a filled outer shell, the balance of repulsion results in a relatively larger atomic size than its ionic counterpart. Understanding electron-electron repulsion provides insight into why ions can have different sizes compared to their neutral atomic forms.