Consider the order `O^(2-) lt F^(+) lt Na^(+) lt Mg^(3+)`. Then correct statement(s) is/are :

Options

A. Increasing order of `Z_(eff)`
B. Increasing order of size
C. Increasing order of I.E.
D. Increasing order of E.A.

Explanation

To analyze the order \( O^{2-} < F^{+} < Na^{+} < Mg^{3+} \) and determine the correct statements, we will consider the effective nuclear charge, ionic sizes, and electron affinities of the ions involved.

### Step-by-Step Solution:

1. **Identify the Ions and Their Electron Configurations:**
- \( O^{2-} \): Has gained 2 electrons, total of 10 electrons (same as Ne).
- \( F^{+} \): Has lost 1 electron, total of 9 electrons.
- \( Na^{+} \): Has lost 1 electron, total of 10 electrons (same as Ne).
- \( Mg^{3+} \): Has lost 3 electrons, total of 10 electrons (same as Ne).

2. **Determine the Effective Nuclear Charge (Z_eff):**
- The effective nuclear charge increases with the number of protons in the nucleus.
- \( O^{2-} \) has 8 protons, \( F^{+} \) has 9 protons, \( Na^{+} \) has 11 protons, and \( Mg^{3+} \) has 12 protons.
- The effective nuclear charge affects the size of the ions: more protons lead to a stronger attraction of electrons, resulting in a smaller ionic radius.

3. **Analyze the Ionic Sizes:**
- The ionic size decreases with increasing positive charge and increases with increasing negative charge.
- Therefore, the order of size based on effective nuclear charge is:
- \( O^{2-} > F^{+} > Na^{+} > Mg^{3+} \)
- This confirms the order \( O^{2-} < F^{+} < Na^{+} < Mg^{3+} \) in terms of increasing size.

4. **Consider Electron Affinities:**
- Electron affinity is the energy change when an electron is added to a neutral atom.
- \( O^{2-} \) is less stable than \( F^{+} \) because it has a higher negative charge and is less favorable to gain another electron.
- The order of electron affinity (from most favorable to least) is:
- \( F > Na > Mg > O \)
- This indicates that \( O^{2-} \) has the least favorable electron affinity.

5. **Conclusion:**
- The correct order based on size is \( O^{2-} > F^{+} > Na^{+} > Mg^{3+} \).
- The order \( O^{2-} < F^{+} < Na^{+} < Mg^{3+} \) is indeed correct in terms of increasing size.