What is the correct increasing order of ionic atomic radii in the following ?

Options

A. `Si^(4+)ltP^(5+)ltS^(6+)ltCl^(7+)`
B. `P^(5+)ltSi^(4+)ltCl^(7+) lt S^(6+)`
C. `Cl^(7+) lt S^(6+)ltP^(5+) lt Si^(4+)`
D. `S^(6+)ltP^(5+)ltCl^(7+)lt Si^(4+)`

Answer

To determine the correct increasing order of ionic atomic radii for the ions Si⁴⁺, P⁵⁺, S⁶⁺, and Cl⁷⁺, we can follow these steps:

### Step 1: Identify the Ions and Their Electron Configurations
- **Silicon (Si)**: Atomic number = 14, Si⁴⁺ has 10 electrons (1s² 2s² 2p⁶).
- **Phosphorus (P)**: Atomic number = 15, P⁵⁺ has 10 electrons (1s² 2s² 2p⁶).
- **Sulfur (S)**: Atomic number = 16, S⁶⁺ has 10 electrons (1s² 2s² 2p⁶).
- **Chlorine (Cl)**: Atomic number = 17, Cl⁷⁺ has 10 electrons (1s² 2s² 2p⁶).

### Step 2: Determine Isoelectronic Species
All the ions (Si⁴⁺, P⁵⁺, S⁶⁺, Cl⁷⁺) are isoelectronic, meaning they have the same number of electrons (10 electrons).

### Step 3: Analyze Ionic Radii Based on Charge
The ionic radius is inversely proportional to the charge of the ion. This means that as the positive charge increases, the ionic radius decreases.

- **Cl⁷⁺**: Highest positive charge, smallest radius.
- **S⁶⁺**: Next highest positive charge, larger than Cl⁷⁺.
- **P⁵⁺**: Next, larger than S⁶⁺.
- **Si⁴⁺**: Lowest positive charge, largest radius.

### Step 4: Write the Increasing Order of Ionic Radii
Based on the analysis:
- Cl⁷⁺ < S⁶⁺ < P⁵⁺ < Si⁴⁺

Thus, the correct increasing order of ionic atomic radii is:
**Cl⁷⁺ < S⁶⁺ < P⁵⁺ < Si⁴⁺**

### Step 5: Verify with Options
After reviewing the options provided, the correct answer corresponds to the order derived above.

### Final Answer
The correct increasing order of ionic atomic radii is:
**Cl⁷⁺ < S⁶⁺ < P⁵⁺ < Si⁴⁺**

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