Step 1: Understanding the Concept:
Isoelectronic species are atoms or ions that have the same number of electrons. For such species, the size is determined by the nuclear charge (number of protons). A higher nuclear charge pulls the same number of electrons closer to the center, making the ion smaller.
Step 2: Detailed Explanation:
1. Both $Cl^{-}$ and $K^{+}$ have 18 electrons.
2. Nuclear Charge (Protons):
- $Cl$ has 17 protons.
- $K$ has 19 protons.
3. Since $K^{+}$ has more protons (19) than $Cl^{-}$ (17), the nucleus of $K^{+}$ exerts a stronger attractive force on its 18 electrons.
4. This stronger attraction pulls the electron cloud inward, making $K^{+}$ smaller and $Cl^{-}$ relatively larger.
Step 3: Final Answer
$Cl^{-}$ ion is bigger than $K^{+}$ ion.