Answer:
Choice number two. The value of "X" in this equation should be constant for all elements across a period.
Explanation:
Electrons are negative while protons are positive. Electrons are attracted to the proton but repel each other.
Consider an atom where electrons occupy more than one energy level. Consider the Bohr Model for that atom. Protons in the nucleus attract the electrons towards the center of the atom. However, at the same time, electrons in the inner shell will repel the valence electrons. That creates an outward force that pushes the valence electrons away from the atom.
The two forces mostly balance each other, but the attraction is slightly stronger. As a result, the overall force on the valence electrons is attractive. The effective nuclear charge gives the number of protons required to produce an attraction of that strength if there was no repulsion at all.
The value of effective nuclear charge is approximately the same as atomic number minus the number of inner-shell electrons. Apparently, the "X" in this question stands for the number of inner-shell electrons.
By the Aufbau Principle, all spots in the inner shell must be filled before more electrons can be added. Additionally, atoms in the same period have the same number of inner shells. As a result, the number of inner-shell electrons will be the same for all atoms in each period. Hence, the value of "X" should stay (approximately) the same across each period.
