Which of the following is arranged in decreasing order of size?

Options

A. `Mg^(2+) gt Al^(3+) gt O^(2-)`
B. `O^(2-) gt Mg^(2+) gt Al^(3+)`
C. `Al^(3+) gt Mg^(2+) gt O^(-)`
D. `Al^(3+) gt O^(2-) gt Mg^(2+)`

Answer

To determine the decreasing order of size for the given ions, we need to analyze the sizes of the ions based on their charges and the general trends in ionic sizes.

### Step-by-Step Solution:

1. **Identify the Ions**: We have three species to compare: \( \text{Mg}^{2+} \), \( \text{Al}^{3+} \), and \( \text{O}^{2-} \).

2. **Understand Ionic Sizes**:
- **Cations** (positively charged ions) are smaller than their neutral atoms. The greater the positive charge, the smaller the cation. This is because a higher positive charge pulls the electrons closer to the nucleus, reducing the size.
- **Anions** (negatively charged ions) are larger than their neutral atoms. The greater the negative charge, the larger the anion. This is because additional electrons increase electron-electron repulsion, causing the size to increase.

3. **Compare the Cations**:
- **Magnesium Ion (\( \text{Mg}^{2+} \))**: This ion has a charge of +2. It is smaller than its neutral magnesium atom.
- **Aluminum Ion (\( \text{Al}^{3+} \))**: This ion has a charge of +3. It is smaller than its neutral aluminum atom and smaller than \( \text{Mg}^{2+} \) because it has a higher positive charge.

4. **Compare the Anion**:
- **Oxide Ion (\( \text{O}^{2-} \))**: This ion has a charge of -2. It is larger than its neutral oxygen atom because it has gained electrons, resulting in increased size due to electron-electron repulsion.

5. **Establish the Size Order**:
- Since \( \text{O}^{2-} \) is an anion, it will be larger than both cations.
- Between the cations, \( \text{Mg}^{2+} \) is larger than \( \text{Al}^{3+} \) because \( \text{Al}^{3+} \) has a higher positive charge.

6. **Final Order**: Therefore, the decreasing order of size is:
\[ \text{O}^{2-} > \text{Mg}^{2+} > \text{Al}^{3+} \]

### Conclusion:
The correct arrangement in decreasing order of size is:
\[ \text{O}^{2-} > \text{Mg}^{2+} > \text{Al}^{3+} \]