The radius of isoelectronic species

Options

A. Increases with increase in nuclear charge
B. Decreases with increases in nuclear charge
C. Same for all
D. First increases and then decreases

Answer

To determine the radius of isoelectronic species, we need to understand how nuclear charge affects the size of these species. Isoelectronic species are atoms or ions that have the same number of electrons but may differ in the number of protons (nuclear charge).

### Step-by-Step Solution:

1. **Understand Isoelectronic Species**:
- Isoelectronic species have the same electron configuration but different nuclear charges. For example, O²⁻, F⁻, Ne, Na⁺, and Mg²⁺ are all isoelectronic with 10 electrons.

2. **Effect of Nuclear Charge**:
- The nuclear charge refers to the total charge of the nucleus, which is determined by the number of protons. An increase in nuclear charge means that there are more protons in the nucleus, which increases the positive charge.

3. **Attraction Between Nucleus and Electrons**:
- As the nuclear charge increases, the attraction between the positively charged nucleus and the negatively charged electrons also increases. This stronger attraction pulls the electrons closer to the nucleus.

4. **Impact on Atomic Radius**:
- As a result of the increased attraction due to higher nuclear charge, the size of the electron cloud (atomic radius) decreases. Therefore, with an increase in nuclear charge, the radius of isoelectronic species decreases.

5. **Evaluating the Options**:
- **Option 1**: "Increases with increase in nuclear charge" - Incorrect, as we established that the radius decreases.
- **Option 2**: "Decreases with increase in nuclear charge" - Correct, as the radius does decrease.
- **Option 3**: "Same for all" - Incorrect, because different nuclear charges result in different radii.
- **Option 4**: "First increases then decreases" - Incorrect, as there is no such trend in isoelectronic species.

### Conclusion:
The correct option is that the radius of isoelectronic species **decreases with an increase in nuclear charge**.

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