Answer
For an electron in $n=3$, $$Z_{eff}(Mg)\lt Z_{eff}(P)\lt Z_{eff}(K)\lt Z_{eff}(Ti)\lt Z_{eff}(Rh)$$
Work Step by Step
We know that the effective nuclear charge $Z_{eff}$ for an electron would increase from left to right in a row in the periodic table, for the increase in nuclear charge. Therefore,
- Row 3: $Z_{eff}(P)\gt Z_{eff}(Mg)$
- Row 4: $Z_{eff}(Ti)\gt Z_{eff}(K)$
Also, as we go down in the periodic table, the nuclear charge would dramatically increase, while the screening effect is almost the same for electrons in $n=3$, since the number of electrons in $n=1,2, 3$ stays the same. So, the effective nuclear charge would increase as we go down.
Therefore, for an electron in $n=3$, $$Z_{eff}(Mg)\lt Z_{eff}(P)\lt Z_{eff}(K)\lt Z_{eff}(Ti)\lt Z_{eff}(Rh)$$
