Which of the following is correct prder of `Z_(eff)`:

Options

A. `I^(-) gt I gt I^(+)`
B. `Mg^(2+) gt Na^(+) gt F^(-)`
C. `P^(5+) lt P^(3+)`
D. `Li gt Be gt B`

Answer

To determine the correct order of effective nuclear charge (Z_eff) among the given species, we need to analyze each option based on the principles of effective nuclear charge and isoelectronic species.

### Step-by-Step Solution:

1. **Understanding Effective Nuclear Charge (Z_eff)**:
- Z_eff is the net positive charge experienced by an electron in a multi-electron atom. It accounts for the actual nuclear charge (number of protons) minus the shielding effect of other electrons.
- The formula for Z_eff can be approximated as:
\[ Z_{eff} = Z - S \]
where \( Z \) is the atomic number and \( S \) is the shielding constant.

2. **Analyzing the First Option (I^-, I, I^+)**:
- All three species have the same nucleus (Iodine) but differ in the number of electrons.
- I^- has 53 electrons, I has 53 electrons, and I^+ has 52 electrons.
- As the number of electrons decreases, Z_eff increases.
- Therefore, the order is: I^+ > I > I^-.
- This option is incorrect as it does not match the given order.

3. **Analyzing the Second Option (Mg^2+, Na^+, S^-)**:
- All three species are isoelectronic with 10 electrons (Ne configuration).
- The atomic numbers are: Mg (12), Na (11), and S (16).
- Since Mg has the highest number of protons, it will have the highest Z_eff.
- Therefore, the order is: Mg^2+ > Na^+ > S^-.
- This option is correct.

4. **Analyzing the Third Option (P^5+, P^3+, P)**:
- All three species are the same element (Phosphorus) but differ in charge.
- P^5+ has 15 protons and 10 electrons, P^3+ has 15 protons and 12 electrons, and P has 15 protons and 15 electrons.
- The effective nuclear charge increases with the positive charge, so the order is: P^5+ > P^3+ > P.
- This option is incorrect.

5. **Analyzing the Fourth Option (Li, Be, B)**:
- These are elements in the same period (2nd period).
- As we move across a period from Li to Be to B, the effective nuclear charge increases due to an increase in protons while the shielding effect remains relatively constant.
- Therefore, the order is: B > Be > Li.
- This option is incorrect.

6. **Conclusion**:
- The only correct order of Z_eff is found in the second option: Mg^2+ > Na^+ > S^-.

### Final Answer:
The correct order of Z_eff is: **Mg^2+ > Na^+ > S^-**.