Periodic Properties

One Cause, Many Trends

Almost every periodic trend follows from the effective nuclear charge $Z_{\text{eff}}$, the net positive pull an outer electron actually feels, once inner electrons have screened part of the nuclear charge:

$$Z_{\text{eff}} = Z - S$$

where $S$ is the shielding constant. Core electrons shield well; electrons in the same shell shield each other only weakly.

Across a period (left to right), $Z$ rises by one per element while the new electrons enter the same shell and barely shield each other. $Z_{\text{eff}}$ therefore climbs steadily, pulling the outer shell inward. Down a group, each step adds a whole new shell and a full core of shielding electrons, so $Z_{\text{eff}}$ stays roughly constant while $n$ jumps.

Ionisation energy is the energy to remove the outermost electron. Successive ionisations always cost more, and there is a huge jump the moment you break into a full core, that jump is how the group number can be read off experimental data. Two irregularities are worth knowing: boron dips below beryllium because its electron leaves a higher $2p$ rather than a filled $2s$, and oxygen dips below nitrogen because its fourth $2p$ electron must pair up and suffer extra repulsion.

Cations are always smaller than their parent atom, losing an electron often empties a whole shell and leaves the rest more tightly held. Anions are always larger, because the added electron increases repulsion without increasing $Z$.

Common pitfall: explaining "atoms get smaller across a period" by saying electrons are added. Electrons are indeed added, but they enter the same shell and shield poorly, so the rising nuclear charge wins. It is the proton count, felt through weak shielding, that shrinks the atom.