Shielding and Penetration

Electromagnetic interactions between electrons in an atom modify the effective nuclear charge (Zeff) on each electron. Penetration refers to the presence of an electron inside the shell of an inner electron, and shielding is the process by which an inner electron masks an outer electron from the full attractive force of the nucleus, decreasing Zeff

. Differences in orbital characteristics dictate differences in shielding and penetration. Within the same energy level (indicated by the principle quantum number, n), due to their relative proximity to the nucleus, s-orbital electrons both penetrate and shield more effectively than p-orbital electrons, and p electrons penetrate and shield more effectively than d-orbital electrons. Shielding and penetration along with the effective nuclear charge determine the size of an ion. An overly-simplistic but useful conceptualization of effective nuclear charge is given by the following equation:

Zeff=Z−S

where Z is the number of protons in the nucleus of an atom or ion (the atomic number), and S is the number of core electrons.

Figure 1  illustrates how this equation can be used to estimate the effective nuclear charge of sodium:

Figure 1 : Shielding of the valence electrons by the core electrons