Which of the following statements is`//are` correct ?

Options

A. `Z_("eff")` of elements increases along the period `(rarr)`.
B. `Z_("eff")` of elements increases down the group `(darr)`.
C. Isoelectronic species have the same nuclear charge.
D. Screening constant `(sigma)` increases down the group `(darr)`.

Answer

To determine which statements are correct regarding effective nuclear charge (Z effective) and related concepts, we will analyze each statement step by step.

### Step 1: Understanding Z effective
- **Definition**: Z effective (effective nuclear charge) is defined as the actual nuclear charge (Z) minus the screening constant (σ).
- **Formula**: Z effective = Z - σ

### Step 2: Analyze Statement 1
- **Statement**: "Z effective of elements increases along the period."
- **Explanation**: As we move across a period from left to right, the atomic number (Z) increases by one for each element. The number of inner shell electrons (which contribute to σ) does not increase significantly. Therefore, since Z increases and σ remains relatively constant, Z effective increases.
- **Conclusion**: This statement is **correct**.

### Step 3: Analyze Statement 2
- **Statement**: "Z effective of elements increases down the group."
- **Explanation**: As we move down a group, both Z and σ increase. However, they increase in similar proportions, which means that the effective nuclear charge (Z effective) does not significantly change. Thus, Z effective does not increase down the group.
- **Conclusion**: This statement is **incorrect**.

### Step 4: Analyze Statement 3
- **Statement**: "Isoelectronic species have the same nuclear charge."
- **Explanation**: Isoelectronic species are atoms or ions that have the same number of electrons but may have different nuclear charges. For example, O²⁻, Ne, and Na⁺ are all isoelectronic with 10 electrons, but they have different nuclear charges (8, 10, and 11 respectively).
- **Conclusion**: This statement is **incorrect**.

### Step 5: Analyze Statement 4
- **Statement**: "Screening constant σ increases down the group."
- **Explanation**: As we move down a group, the number of electron shells increases, which leads to an increase in the screening effect. Each additional shell contributes to the screening constant, thus σ increases down the group.
- **Conclusion**: This statement is **correct**.

### Final Summary of Statements:
1. **Correct**: Z effective of elements increases along the period.
2. **Incorrect**: Z effective of elements increases down the group.
3. **Incorrect**: Isoelectronic species have the same nuclear charge.
4. **Correct**: Screening constant σ increases down the group.

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

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