Arrange the following ions in order of their decreasing ionic radii.
`Li^(o+), K^(o+), Mg^(2+), Al^(3+)`

Explanation

To arrange the ions \( \text{Li}^+, \text{K}^+, \text{Mg}^{2+}, \text{Al}^{3+} \) in order of their decreasing ionic radii, we can follow these steps:

### Step 1: Understand the Charge and Size Relationship
Ionic size is influenced by the charge of the ion and its position in the periodic table. Cations (positively charged ions) tend to decrease in size as their positive charge increases due to the increased nuclear charge pulling the electrons closer to the nucleus.

### Step 2: Identify the Ions and Their Charges
- \( \text{Li}^+ \): Lithium ion with a +1 charge.
- \( \text{K}^+ \): Potassium ion with a +1 charge.
- \( \text{Mg}^{2+} \): Magnesium ion with a +2 charge.
- \( \text{Al}^{3+} \): Aluminum ion with a +3 charge.

### Step 3: Compare the Ions Based on Their Charges
- Both \( \text{Li}^+ \) and \( \text{K}^+ \) have a +1 charge, but \( \text{K}^+ \) is larger than \( \text{Li}^+ \) because potassium is located below lithium in Group 1 of the periodic table, and ionic size increases down a group.
- \( \text{Mg}^{2+} \) is smaller than \( \text{Li}^+ \) and \( \text{K}^+ \) because it has a +2 charge, which pulls the electrons closer to the nucleus, resulting in a smaller ionic radius.
- \( \text{Al}^{3+} \) is the smallest among these ions because it has the highest charge (+3), leading to the greatest effective nuclear charge and the smallest ionic radius.

### Step 4: Arrange the Ions in Decreasing Order of Ionic Radii
Based on the analysis:
1. \( \text{K}^+ \) (largest)
2. \( \text{Li}^+ \)
3. \( \text{Mg}^{2+} \)
4. \( \text{Al}^{3+} \) (smallest)

### Final Answer:
The order of the ions in decreasing ionic radii is:
\[ \text{K}^+ > \text{Li}^+ > \text{Mg}^{2+} > \text{Al}^{3+} \]

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