Explain how the effects of nuclear charge and the increasing number of core electrons in an atom oppose each other.

The nulear charge is the number of protons.

As the number of protons increases, the nuclear charge grows ant thhe pulling electrostatic force between them and electrons also grows, given that the electrostatic force is proportional to the magnitude of the charges.

As the number of electrons grows, they occupy outer shelss (farther from the nucleus). And the outer electrons will feel not only the atraction of the protons from the nucleus, but the repulsion of the inner electrons.

Then, we see that the increase of nuclear charge is opposed by the increase of core electrons, and the outer (valence) electrons are not so tied to the nucleus as the core electrons are.

This is called shielding effect. A way to quantify the shielding effect is through the effective nuclear charge which is the number of protons (Z) less the number of core electrons.

The more the number of core shells the greater the shielding effect experience by electros in the outermost shells.

The shielding effect, explains why the valence eletrons are more easily removed from the atom than core electrons, and also explains some  trends of the periodic table: variationof the size of the atoms in a row, the greater the shielding efect, the less the atraction force felt by the outermos electron, the farther they are and the larger the atom.