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The stronger the attraction, and the stronger z e f f, the closer the electrons are pulled toward the nucleus. The concept of effective nuclear charge (zeff) represents a fundamental principle in atomic physics that helps explain periodic trends in atomic properties, particularly ionization energy. As you move across a period (left to right), the ionization energy generally increases due to the increasing effective nuclear charge, making it more challenging to remove outer electrons. $z_ {eff}$ is certainly a major factor in determining ionization energies, however atomic and ionic radius probably shouldn't be viewed as having a direct causative relationship to ionization energy.
For an atom or an ion with only a single electron, we can calculate the potential energy by considering only the electrostatic attraction between the positively charged nucleus and the negatively charged electron. By developing robust models for zeff calculation, we aim to enhance predictive capabilities for ionization energies without requiring extensive experimental measurements. Slater's rules are fairly simple and produce fairly accurate predictions of things like the electron configurations and ionization energies. Ionization energy exhibits a direct correlation with zeff, as elements with higher effective nuclear charge require more energy to remove an electron from the atom.
The term effective is used because the shielding effect of negatively charged electrons prevent higher energy electrons from experiencing the full nuclear charge of the nucleus due to the repelling effect of inner layer. Understanding electron shielding is essential for predicting trends in atomic size and ionization energy This figure illustrates how the effective nuclear charge experienced by outer electrons varies across the first three rows of the periodic table.
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