Of the following the ion with the smallest ionic radius is

Options

A. `K^(+)`
B. `Ca^(2+)`
C. `Ti^(3+)`
D. `Ti^(4+)`

Explanation

To determine which ion has the smallest ionic radius among the given options (K⁺, Ca²⁺, Ti³⁺, and Ti⁴⁺), we can follow these steps:

### Step-by-step Solution:

1. **Understand Ionic Radii**: Ionic radius is the measure of an atom's ion in a crystal lattice. It is influenced by the charge of the ion and the number of electrons.

2. **Identify the Ions**: The ions provided are:
- K⁺ (Potassium ion)
- Ca²⁺ (Calcium ion)
- Ti³⁺ (Titanium ion with a +3 charge)
- Ti⁴⁺ (Titanium ion with a +4 charge)

3. **Consider the Charge of the Ions**: As the positive charge of an ion increases, the ionic radius tends to decrease. This is because a higher positive charge means a greater effective nuclear charge, which pulls the electrons closer to the nucleus.

4. **Analyze Each Ion**:
- **K⁺**: Has a +1 charge.
- **Ca²⁺**: Has a +2 charge.
- **Ti³⁺**: Has a +3 charge.
- **Ti⁴⁺**: Has a +4 charge.

5. **Rank the Ions by Charge**: The order of increasing ionic radius based on the charge is:
- K⁺ > Ca²⁺ > Ti³⁺ > Ti⁴⁺

6. **Conclusion**: Since Ti⁴⁺ has the highest positive charge (+4), it will have the smallest ionic radius among the given ions.

### Final Answer:
The ion with the smallest ionic radius is **Ti⁴⁺ (Titanium ion with a +4 charge)**.

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