1. Concept used: Fajans' rule
   The polarizing power of a cation depends on its charge/size ratio.

   • Higher positive charge $\Rightarrow$ greater polarizing power
   • Smaller ionic size $\Rightarrow$ greater polarizing power

   So, polarizing power increases with: $\text{Polarizing power} \propto \frac{\text{charge}}{\text{size}}$

2. Compare the given cations

   Given species: $K^+,\ Ca^{2+},\ Mg^{2+},\ Be^{2+}$

   • $K^+$ has only $+1$ charge and relatively large size, so it has the least polarizing power.
   • Among the doubly charged cations, smaller size means greater polarizing power.

3. Size trend

   Ionic sizes decrease roughly as: $Ca^{2+} > Mg^{2+} > Be^{2+}$

   Since all three have the same charge $+2$, their polarizing power increases as size decreases: $Ca^{2+} < Mg^{2+} < Be^{2+}$

4. Combine both effects

   Since $K^+$ has lower charge and larger size than the others, it comes first: $K^+ < Ca^{2+} < Mg^{2+} < Be^{2+}$

5. Match with options

   This corresponds to Option B.

Final Answer: $K^+ < Ca^{2+} < Mg^{2+} < Be^{2+}$