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

Options

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

Explanation

To analyze the order \( O^{2-} < F^{-} < Na^{+} < Mg^{2+} \) and determine the correct statements regarding effective nuclear charge (Z_eff), size, ionization energy, and electron affinity, we can follow these steps:

### Step 1: Understand the Species
- Identify the species involved:
- \( O^{2-} \): Oxygen ion with a charge of -2 (gains 2 electrons).
- \( F^{-} \): Fluorine ion with a charge of -1 (gains 1 electron).
- \( Na^{+} \): Sodium ion with a charge of +1 (loses 1 electron).
- \( Mg^{2+} \): Magnesium ion with a charge of +2 (loses 2 electrons).

### Step 2: Determine the Number of Electrons and Protons
- Count the protons and electrons for each ion:
- \( O^{2-} \): 8 protons, 10 electrons.
- \( F^{-} \): 9 protons, 10 electrons.
- \( Na^{+} \): 11 protons, 10 electrons.
- \( Mg^{2+} \): 12 protons, 10 electrons.

### Step 3: Analyze the Ionic Sizes
- The size of the ions generally decreases with an increase in positive charge and increases with an increase in negative charge due to electron-electron repulsion.
- Therefore, the order of ionic sizes is:
- \( O^{2-} > F^{-} > Na^{+} > Mg^{2+} \)
- This means the order given in the question is actually the decreasing order of size.

### Step 4: Evaluate the Effective Nuclear Charge (Z_eff)
- The effective nuclear charge increases with the number of protons while the number of electrons remains constant.
- Since the order of protons is \( 8 < 9 < 11 < 12 \), the effective nuclear charge also increases in the same order:
- \( O^{2-} < F^{-} < Na^{+} < Mg^{2+} \)

### Step 5: Analyze Ionization Energy
- Ionization energy is inversely related to the size of the ion. As size decreases, ionization energy increases.
- Since the size order is \( O^{2-} > F^{-} > Na^{+} > Mg^{2+} \), the order of ionization energy will be:
- \( O^{2-} < F^{-} < Na^{+} < Mg^{2+} \) (increasing order).

### Step 6: Analyze Electron Affinity
- Electron affinity generally increases with decreasing size and increasing effective nuclear charge.
- Thus, the order of electron affinity will also follow the same increasing order:
- \( O^{2-} < F^{-} < Na^{+} < Mg^{2+} \).

### Conclusion
Based on the analysis:
1. **Increasing order of Z_eff**: Correct
2. **Increasing order of size**: Incorrect (it's decreasing)
3. **Increasing order of ionization energy**: Correct
4. **Increasing order of electron affinity**: Correct

### Final Answer
The correct statements are: 1, 3, and 4.

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