Question

Describe the relationship between a. the radius of a cation and that of the atom from which forms b. the radius of an anion and that of the atom from which it forms

Short answer

The radius of a cation is smaller than its neutral atom because it loses electrons, increasing the effective nuclear charge on electrons. The radius of an anion is larger than its neutral atom because it gains electrons, leading to increased electron-electron repulsion.

Step-by-step solution

Understanding the Formation of Cations

A cation is formed when an atom loses one or more electrons. Losing electrons reduces electron-electron repulsion and allows remaining electrons to be drawn closer to the nucleus, resulting in a smaller atomic radius compared to the neutral atom.

Comparing the Radius of a Cation with its Neutral Atom

The radius of a cation is smaller than the radius of the original neutral atom from which it forms. This is because when electrons are removed, the effective nuclear charge on the remaining electrons increases, pulling them closer to the nucleus and reducing the size of the ion.

Understanding the Formation of Anions

An anion is formed when an atom gains one or more electrons. Gaining electrons increases electron-electron repulsion, which can't be fully compensated by the nuclear attraction on the added electrons, leading to a generally larger atomic radius compared to the neutral atom.

Comparing the Radius of an Anion with its Neutral Atom

The radius of an anion is larger than the radius of the original neutral atom from which it forms. This is due to the addition of electrons, which increases repulsion among the electrons and causes the electron cloud to expand.

Key concepts

Cation Formation

When an atom loses one or more of its electrons, it becomes a positively charged ion known as a cation. This process typically occurs when atoms interact and one is more electronegative than the other, causing it to take electrons away. During this process, the atom that loses electrons experiences a decrease in the electron-electron repulsion which previously kept the electrons relatively far apart. With fewer electrons pushing against each other, the remaining electrons can be pulled closer to the nucleus by its positive charge.
This is due to an increase in the effective nuclear charge per electron. Since the nucleus has not changed (the number of protons remains constant), the reduction in the number of electrons means that each remaining electron feels a stronger pull towards the center. The overall effect is that the radius of a cation is smaller than the radius of the neutral atom it originated from.

Anion Formation

On the other end of the spectrum, anions are formed when an atom gains electrons, thus acquiring a negative charge. This can occur when an atom comes into contact with another one that has a relatively lower affinity for electrons. As the atom gains extra electrons, the increased electron-electron repulsion within the electron cloud forces the electrons to spread out more than they did in the neutral atom.
With more electrons in the cloud, each electron now experiences a weaker effective nuclear charge, because the additional electrons shield one another from the full attraction of the nucleus. Consequently, the atomic radius of an anion is larger than the atomic radius of the original, neutral atom. The expansion of the electron cloud outweighs the nuclear attraction on the added electrons, leading to the overall increase in size.

Effective Nuclear Charge

The effective nuclear charge (Z_eff) is the net positive charge experienced by an electron in a poly-electron atom. It's like a balancing act between the attraction from the protons in the nucleus and the repulsion from other electrons. As electrons are added or removed from an atom, the effective nuclear charge on the remaining electrons changes. When an atom becomes a cation, the loss of electron(s) increases the Z_eff, allowing the protons to exert more influence over the remaining electrons, and thus, shrink the ion. Conversely, when an atom becomes an anion by gaining electrons, the Z_eff decreases because the additional electrons provide more shielding. This makes the nucleus seem less powerful to the outermost electrons and the anion becomes larger.

Electron-Electron Repulsion

Electron-electron repulsion is a fundamental concept that explains the forces at play within the electron cloud of an atom. As negatively charged particles, electrons naturally repel one another due to their like charges. This repulsion is responsible for the shape and size of the electron cloud as electrons try to maintain as much distance from each other as possible while still being attracted to the positively charged nucleus.
This principle is directly related to the size changes observed in cation and anion formation. When an atom forms a cation, the reduced number of electrons means less repulsion and a more compact electron cloud. In contrast, the formation of an anion introduces additional electrons, increasing repulsion and causing the cloud to expand. Hence, the radius of an anion is larger than its original atom, while the radius of a cation is smaller.