Answer:
Assuming those contributions to the screening, the [tex]Z_{eff}[/tex] estimation for Si is 4, and for Cl it is 7.
Explanation:
The general expresion for nuclear efective charge is: [tex]Z_{eff}=Z-S[/tex], with Z the atomic number of the element and the number of protons in the nucleus, and S the screening constant.
Si and Cl belong to the third row of the periodic table, so their core electrons are 10 (the same as the noble gas before them, Ne). The number of protons in Si nucleus is 14, and in Cl is 17. Each of the core electrons contribute with 1.00, so each one screens one proton's charge, leaving a total [tex]Z_{eff}[/tex] of 4 for Si and 7 for Cl.
For Si, this aproximation underestimate the experimental value, so probably the valence electrons contribute to the screening (contribution bigger than 0.0). For Cl this value is overestimated, and probably the contribution of the core electrons is weaker than 1.0.