There are two ions, K+ and Cl-. Find the Zeff for 2p for each ion if the valence electrons contribute 0, and the core electrons contribute 1 to S. Now calculate the Zeff of 2p using Slater's rules.
Zeff is better known as the effective nuclear charge. It is the positive charge from a nucleus that an electron feels in an atom with more than one electron present. The further away an electron is from the nucleus, the less charge it will experience due to distance and also the shielding and repulsion effects of neighboring electrons. Zeff can be calculated as follows:
Zeff = Z - S
Z is the number of protons in the nucleus of the atom and S is a measure of the average number of electrons between the nucleus and the particular electron being studied. S can be calculated according to Slater's rules, which assigns a particular value to different types of electrons.
We are looking at the potassium cation (K+) and the chlorine anion (Cl-). The potassium cation has 19 protons in its nucleus. The chlorine anion has 17 protons in its nucleus. For both ions, the 3 shell is the valence shell of electrons. Since we are looking at a 2p electron in both cases, we can tabulate the number of core electrons as those in the 1s, 2s, and 2p shells. This corresponds to 9 total core electrons other than the 2p one we are looking at. So doing the subtraction:
for K+: Zeff=19-9=10
for Cl-: Zeff=17-9=8
This is for your rules, where the core electrons contribute 1 to S and the valence electrons contribute nothing. According to Slater's rules, electrons in the same shell account for 35% of a charge and electrons in the lower shell count for 85% of a charge. So according to Slater's rules:
for K+: Zeff=19-[7*0.85+2*0.85]=19-4.15=14.85
for Cl-: Zeff=17-4.15=12.85