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.