The size of the iso-electronic species `Cl ^(-) , Ar and Ca ^(2+)` is affected by :

Options

A. Azimuthal quantum number of valence shell
B. Electron-electron interaction in the outer orbitals
C. Principal quantum number of valence shell
D. Nuclear charge.

Explanation

To determine how the size of the isoelectronic species \( \text{Cl}^-, \text{Ar}, \text{Ca}^{2+} \) is affected, we need to analyze the factors that influence atomic size in isoelectronic species.

### Step-by-Step Solution:

1. **Understanding Isoelectronic Species**:
- Isoelectronic species are atoms or ions that have the same number of electrons. In this case, \( \text{Cl}^- \) (17 protons, 18 electrons), \( \text{Ar} \) (18 protons, 18 electrons), and \( \text{Ca}^{2+} \) (20 protons, 18 electrons) all have 18 electrons.

2. **Nuclear Charge**:
- The nuclear charge is the total charge of the nucleus, which is determined by the number of protons.
- For \( \text{Cl}^- \), the nuclear charge is +17 (17 protons).
- For \( \text{Ar} \), the nuclear charge is +18 (18 protons).
- For \( \text{Ca}^{2+} \), the nuclear charge is +20 (20 protons).

3. **Effect of Nuclear Charge on Size**:
- The size of the atom is inversely related to the nuclear charge when comparing isoelectronic species. A higher nuclear charge means a stronger attraction between the nucleus and the electrons.
- Thus, \( \text{Ca}^{2+} \) with the highest nuclear charge (+20) will have the smallest size because the electrons are pulled closer to the nucleus.
- Conversely, \( \text{Cl}^- \) with the lowest nuclear charge (+17) will have the largest size because the attraction is weaker, allowing the electrons to be further away from the nucleus.

4. **Conclusion**:
- The size of the isoelectronic species \( \text{Cl}^-, \text{Ar}, \text{Ca}^{2+} \) is primarily affected by the nuclear charge. The greater the nuclear charge, the smaller the size of the ion/atom.

### Final Answer:
The size of the isoelectronic species \( \text{Cl}^-, \text{Ar}, \text{Ca}^{2+} \) is affected by the **nuclear charge**.

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