Which of the following arrangements represents the correct order of increasing radius?

Options

A. `Mg^(2+) lt K^(+) lt Se^(2-) lt S^(2-)`
B. `Mg^(2+) lt K^(+) lt S^(2-) lt Se^(2-)`
C. `Se^(2-) lt S^(2-) lt Mg^(2+) lt K^(+)`
D. `Mg^(2+) lt Se^(2-) lt K^(+) S^(2-)`

Explanation

To determine the correct order of increasing radius among the given ions and atoms, we will follow these steps:

### Step 1: Understand the Trend of Atomic and Ionic Radii
- Atomic and ionic radii generally increase as you move down a group in the periodic table due to the addition of electron shells.
- Conversely, atomic and ionic radii decrease as you move from left to right across a period due to increased nuclear charge, which pulls the electrons closer to the nucleus.

### Step 2: Identify the Species in the Question
- The species mentioned in the problem are: Mg, Mg²⁺, K⁺, Na⁺, S, and Se.

### Step 3: Analyze Each Species
1. **Mg (Magnesium)**: This is a neutral atom.
2. **Mg²⁺ (Magnesium Ion)**: This ion has lost two electrons, resulting in a smaller radius compared to the neutral Mg atom.
3. **K⁺ (Potassium Ion)**: This ion has lost one electron. It is larger than Mg²⁺ but smaller than its parent atom K.
4. **Na⁺ (Sodium Ion)**: This ion has lost one electron and is smaller than both Mg and K.
5. **S (Sulfur)**: This is a neutral atom.
6. **Se (Selenium)**: This is also a neutral atom and is located below sulfur in the periodic table, so it has a larger radius than sulfur.

### Step 4: Compare the Sizes
- From the analysis:
- Mg > Mg²⁺ (Mg is larger than its ion)
- K⁺ > Na⁺ (K⁺ is larger than Na⁺)
- S > Se (S is smaller than Se)

### Step 5: Arrange the Species in Order of Increasing Radius
- The order of increasing radius based on the above comparisons is:
- Mg²⁺ < Na⁺ < K⁺ < Mg < S < Se

### Final Order
Thus, the correct order of increasing radius is:
**Mg²⁺ < Na⁺ < K⁺ < Mg < S < Se**