Arrange the following ions in the increasing order of their size: `Be^(2+), CI^(-), S^(2-), Na^(+), Mg^(2+), Br^(-1)`?

Explanation

To arrange the ions `Be^(2+), Cl^(-), S^(2-), Na^(+), Mg^(2+), Br^(-1)` in increasing order of their size, we need to consider the following:

### Step 1: Identify the Ions and Their Electron Configurations
- **Be^(2+)**: Beryllium ion with 4 protons and 2 electrons (configuration: 1s²).
- **Mg^(2+)**: Magnesium ion with 12 protons and 10 electrons (configuration: 1s² 2s² 2p⁶).
- **Na^(+)**: Sodium ion with 11 protons and 10 electrons (configuration: 1s² 2s² 2p⁶).
- **Cl^(-)**: Chloride ion with 17 protons and 18 electrons (configuration: 1s² 2s² 2p⁶ 3s² 3p⁶).
- **S^(2-)**: Sulfide ion with 16 protons and 18 electrons (configuration: 1s² 2s² 2p⁶ 3s² 3p⁶).
- **Br^(-)**: Bromide ion with 35 protons and 36 electrons (configuration: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 4p⁶).

### Step 2: Determine the Number of Electrons and Protons
- **Isoelectronic Species**: Be^(2+), Mg^(2+), Na^(+), Cl^(-), and S^(2-) all have the same number of electrons (10 or 18).
- The size of isoelectronic species is inversely proportional to the number of protons. More protons mean a smaller ionic radius.

### Step 3: Compare Sizes of Isoelectronic Species
1. **Be^(2+)**: 4 protons → smallest size.
2. **Mg^(2+)**: 12 protons → larger than Be^(2+).
3. **Na^(+)**: 11 protons → larger than Mg^(2+) but smaller than Cl^(-) and S^(2-).
4. **Cl^(-)**: 17 protons → larger than Na^(+) and Mg^(2+).
5. **S^(2-)**: 16 protons → larger than Cl^(-) but smaller than Br^(-).
6. **Br^(-)**: 35 protons → largest size.

### Step 4: Arrange the Ions in Increasing Order of Size
Based on the above analysis, the increasing order of ionic size is:
1. Be^(2+)
2. Mg^(2+)
3. Na^(+)
4. Cl^(-)
5. S^(2-)
6. Br^(-)

### Final Answer
**Increasing order of ionic size**: `Be^(2+) < Mg^(2+) < Na^(+) < Cl^(-) < S^(2-) < Br^(-)`