Chloride ion and potassium ion are isoelectronic. Then
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For isoelectronic species: Radius \(\propto \frac{1}{\text{Atomic Number (Z)}}\). The species with the highest number of protons will always be the smallest.
Step 1: Understanding the Question:
We are comparing the sizes of two isoelectronic species (ions with the same number of electrons). Step 2: Detailed Explanation:
- Chlorine (Atomic number Z = 17) forms Cl\(^{-}\) by gaining 1 electron. Total electrons = 18.
- Potassium (Atomic number Z = 19) forms K\(^{+}\) by losing 1 electron. Total electrons = 18.
Both have 18 electrons, but different nuclear charges (number of protons).
- In Cl\(^{-}\), 17 protons pull 18 electrons.
- In K\(^{+}\), 19 protons pull 18 electrons.
Higher nuclear charge results in a stronger pull on the electrons, making the ion smaller. Therefore, K\(^{+}\) is smaller than Cl\(^{-}\).
Conversely, Cl\(^{-}\) is bigger than K\(^{+}\). Step 3: Final Answer:
Cl\(^{-}\) ion is bigger than K\(^{+}\) ion.