which of the following ions has the smallest radius?

Options

A. `Ti^(2+)`
B. `Pt^(2+)`
C. `Ni^(2+)`
D. `Zr^(2+)`

Answer

To determine which of the given ions has the smallest radius, we will analyze the ionic radii of titanium (Ti), platinum (Pt), nickel (Ni), and zirconium (Zr) after they have been ionized. Here’s a step-by-step solution:

### Step 1: Identify the Atomic Numbers and Electron Configurations
- **Titanium (Ti)**: Atomic number 22; Electron configuration: [Ar] 4s² 3d²
- **Platinum (Pt)**: Atomic number 78; Electron configuration: [Xe] 4f¹⁴ 5d⁹ 6s¹
- **Nickel (Ni)**: Atomic number 28; Electron configuration: [Ar] 4s² 3d⁸
- **Zirconium (Zr)**: Atomic number 40; Electron configuration: [Kr] 5s² 4d²

### Step 2: Determine the Ionization States
We will consider the ions after removing two electrons (2+ state):
- **Ti²⁺**: [Ar] 3d²
- **Pt²⁺**: [Xe] 4f¹⁴ 5d⁸
- **Ni²⁺**: [Ar] 3d⁸
- **Zr²⁺**: [Kr] 4d²

### Step 3: Analyze the Position in the Periodic Table
- **Ti²⁺**: First transition series
- **Ni²⁺**: First transition series
- **Pt²⁺**: Third transition series
- **Zr²⁺**: Fourth transition series

### Step 4: Compare Ionic Radii Trends
1. **General Trend**: Ionic radii decrease across a period and increase down a group.
2. **Transition Metals**: As we move from left to right in the transition series, the effective nuclear charge increases, pulling the electrons closer and resulting in a smaller ionic radius.

### Step 5: Conclusion
- **Comparing the Ions**:
- Ti²⁺ has a larger radius than Ni²⁺ due to being in the same period but with fewer protons.
- Ni²⁺ has a smaller radius than Ti²⁺ and Zr²⁺ due to its higher nuclear charge.
- Pt²⁺ is larger than Ni²⁺ due to being in a higher period despite having a similar electron configuration.
- Zr²⁺ has a larger radius than all due to being in a lower period.

Thus, the smallest ionic radius among the given ions is that of **Ni²⁺**.

### Final Answer
**The ion with the smallest radius is Ni²⁺.**

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