According to Slater's rule , correct order of `Z_("eff")` on valence shell electron is :

Options

A. `Fe gt Fe^(2+) gt Fe^(3+)`
B. `N^(3-) lt O^(2-) lt F^(-)`
C. `Na^(+) lt Mg^(2+) lt Al^(3+)`
D. `Tl^(2+) lt V^(3+) lt Mn^(5+)`

Explanation

To determine the correct order of effective nuclear charge (Z_eff) on valence shell electrons according to Slater's rule, we need to understand a few key concepts.

### Step-by-Step Solution:

1. **Understanding Z_eff**:
- The effective nuclear charge (Z_eff) is defined as the net positive charge experienced by an electron in a multi-electron atom. It is calculated using the formula:
\[ Z_{\text{eff}} = Z - \sigma \]
where \( Z \) is the atomic number (total number of protons) and \( \sigma \) is the screening constant that accounts for the shielding effect of other electrons.

2. **Identifying the Options**:
- The question provides several options for the order of Z_eff for different ions. We need to analyze each option based on the cationic and anionic charges.

3. **Analyzing Each Option**:
- **Option 1**: Fe > Fe²⁺ > Fe³⁺
- Here, Fe has no charge, Fe²⁺ has a +2 charge, and Fe³⁺ has a +3 charge. As the cationic charge increases, Z_eff decreases due to increased shielding. Thus, this option is incorrect.

- **Option 2**: N³⁻ > O²⁻ > F⁻
- N³⁻ has the highest anionic charge, leading to the lowest Z_eff. F⁻ has the least anionic charge, resulting in the highest Z_eff. Therefore, this order is correct.

- **Option 3**: Na⁺ > Mg²⁺ > Al³⁺
- Na⁺ has a +1 charge, Mg²⁺ has a +2 charge, and Al³⁺ has a +3 charge. As the cationic charge increases, Z_eff increases. Thus, this order is also correct.

- **Option 4**: Tl²⁺ > V³⁺ > Mn⁵⁺
- Here, Tl²⁺ has a +2 charge, V³⁺ has a +3 charge, and Mn⁵⁺ has a +5 charge. As the cationic charge increases, Z_eff increases. Therefore, this option is also correct.

4. **Conclusion**:
- According to Slater's rule, the correct orders of Z_eff for the given options are:
- Option 2: N³⁻ > O²⁻ > F⁻
- Option 3: Na⁺ > Mg²⁺ > Al³⁺
- Option 4: Tl²⁺ > V³⁺ > Mn⁵⁺

### Final Answer:
The correct orders of Z_eff on valence shell electrons according to Slater's rule are:
- Option 2, Option 3, and Option 4.