Answer
The effective nuclear charge: $Z_{eff}(Cl^-)=7+$ and $Z_{eff}(K^+)=9+$
Work Step by Step
The formula to calculate $Z_{eff}$ is $$Z_{eff}=Z-S$$
Z: the nuclear charge of the element
S: the screening constant
Both $Cl^-$ and $K^+$ have 18 electrons and the same electron configuration: $1s^22s^22p^63s^23p^6$.
That means both ions have 10 core electrons (n=1 and n=2) and 8 valence electrons (n=3).
Therefore, the screening constant $S$ for both $Cl^-$ and $K^+$ is $$S=10\times1.00+8\times0.00=10.00$$
The nuclear charge of $Cl^-$ is $Z=17+$
The nuclear charge of $K^+$ is $Z=19+$
Therefore, the effective nuclear charge of $Cl^-$ and $K^+$ is
$Z_{eff}(Cl^-)=(17+)-10.00=7+$
$Z_{eff}(K^+)=(19+)-10.00=9+$
