Step 1: Understanding Polarizability
Polarizability refers to the ability of an ion or atom to have its electron cloud distorted by an external electric field. Larger ions with more electrons are generally more polarizable.
Step 2: Analyzing Halide Ions
The halide ions are \( \text{F}^- \), \( \text{Cl}^- \), \( \text{Br}^- \), and \( \text{I}^- \). Their polarizability increases with increasing size and number of electrons.
Step 3: Order of Polarizability
The order of polarizability for halide ions is:
\[
\text{F}^-<\text{Cl}^-<\text{Br}^-<\text{I}^-.
\]
This is because \( \text{I}^- \) is the largest and has the most electrons, making it the most polarizable, while \( \text{F}^- \) is the smallest and least polarizable.
Step 4: Matching with the Options
The correct order \( \text{F}^-<\text{Cl}^-<\text{Br}^-<\text{I}^- \) corresponds to option (D).
Final Answer: The polarizability of halide ions increases in the order \( \text{F}^-<\text{Cl}^-<\text{Br}^-<\text{I}^- \).