Problem 162 - A Complete Resource Book in Chemistry for JEE Main

Question

Which one of the following ion has the highest value of ionic radius? (a) \(\mathrm{F}^{-}\) (b) \(\mathrm{O}^{2-}\) (c) \(\mathrm{B}^{3+}\) (d) \(\mathrm{Li}^{+}\)

Step-by-Step Solution

Answer

The ion \\(\mathrm{O}^{2-}\\) has the highest ionic radius.

Step 1: Understanding Ionic Radii

The ionic radius refers to the size of an ion. In general, as the number of electrons increases relative to protons, the size of the ion increases. Conversely, when electrons are removed, as occurs in cations, the ionic radius decreases.

Step 2: Comparing Anions and Cations

Among the given ions, \(\text{F}^{-}\) and \(\text{O}^{2-}\) are anions (negatively charged), whereas \(\text{B}^{3+}\) and \(\text{Li}^{+}\) are cations (positively charged). Anions generally have larger radii compared to their neutral atoms due to increased electron-electron repulsion, while cations have smaller radii due to the loss of electrons.

Step 3: Identifying Highest Ionic Radius

Between \(\text{F}^{-}\) and \(\text{O}^{2-}\), \(\text{O}^{2-}\) has more additional negative charge (more extra electrons overall) compared to its corresponding neutral atom, resulting in a larger expansion of the electron cloud. Between \(\text{B}^{3+}\) and \(\text{Li}^{+}\), \(\text{Li}^{+}\) is smaller because the loss of electrons causes a higher effective nuclear charge relative to the remaining electron. Hence, \(\text{O}^{2-}\) has the largest ionic radius among the given choices.

Key Concepts

Anions vs Cations

In the world of chemistry, ions are formed when atoms gain or lose electrons. This leads to two main categories: anions and cations.

• Anions: These are negatively charged ions, created when an atom gains one or more electrons. This gain increases the electron-electron repulsion within the ion, generally causing the atom to expand in size and thus have a larger ionic radius than its neutral form.
• Cations: These are positively charged ions, formed when an atom loses electrons. This loss reduces electron-electron repulsion and can result in a smaller ionic radius compared to the atom's neutral form.

For example, in the options given, both - F^{-} and - O^{2-} are anions, while - B^{3+} and - Li^{+} are cations. It is essential to recognize this distinction hence anions tend to have larger ionic radii than cations.

Electron-Electron Repulsion

Inside an atom or ion, electrons occupy several shells around the nucleus. When electrons are added, particularly in anions, they occupy additional space within these shells.

• This increases the overall electron cloud size, resulting in more electron-electron repulsion.
• This repulsion pushes the electrons further apart, expanding the size of the ion.

An excellent example here is the difference between O^{2-} and F^{-} . The former has more electrons, increasing repulsion further, thereby giving a larger ionic radius. This increased repulsion causes O^{2-} to have a significantly larger ionic radius compared to its neutral atom, and even more so compared to cations which have lost electrons.

Effective Nuclear Charge

Effective nuclear charge refers to the net positive charge experienced by an electron in a multi-electron atom or ion. It plays a crucial role in determining an atom's or ion's size.

• As electrons are removed to form cations, the effective nuclear charge on the remaining electrons increases because there are fewer electrons to shield each other from the nucleus.
• This stronger attraction pulls the electrons closer to the nucleus, reducing the ionic radius.

In contrast, for anions, the added electrons increase shielding and repulsion, thus decreasing the effective nuclear charge per electron, but increasing the overall size due to expanded electron clouds. Hence, while Li^{+} is small due to a high effective nuclear charge, O^{2-} is large because the additional electrons disperse the charge, resulting in less control from the nucleus over the widely distributed electrons.