(e) Electronegativity

Fig. 3.7 is a schematic periodic table that summarises the two fundamental trends in atomic properties — how they change as you move across a period (left to right) and down a group (top to bottom). The figure uses colour-coded arrows to show the direction of increase or decrease for each property.

Across a period, the arrows point in one direction: atomic radius decreases; ionisation enthalpy, electron gain enthalpy, and electronegativity all increase; non-metallic character increases. Down a group, the arrows reverse: atomic radius increases; ionisation enthalpy, electron gain enthalpy, and electronegativity all decrease; metallic character increases.

The physical idea is simple but powerful. As you go across a period, electrons are added to the same valence shell, but the nuclear charge (number of protons) increases. The effective nuclear charge experienced by the outermost electrons rises, pulling them closer to the nucleus. That is why the atom shrinks, and why it becomes harder to remove an electron (higher ionisation enthalpy), more favourable to gain an electron (more negative electron gain enthalpy), and stronger at attracting bonding electrons (higher electronegativity). The element becomes less metallic and more non-metallic.

Down a group, a new principal energy level (shell) is added. The valence electrons are farther from the nucleus, and the inner electrons shield them from the full nuclear pull. So the atom grows larger, the outermost electron is easier to remove (lower ionisation enthalpy), the atom is less eager to gain an electron (less negative electron gain enthalpy), and its pull on bonding electrons weakens (lower electronegativity). The element becomes more metallic.

The textbook develops no single formula directly from this figure, but the trends are explained using the concept of effective nuclear charge, $Z_{\text{eff}}$, which is the net positive charge experienced by an electron after accounting for shielding by inner electrons. A simple approximation is:

where $Z$ is the atomic number (number of protons) and $\sigma$ is the shielding constant (a measure of how much inner electrons block the nuclear charge). Across a period, $Z$ increases faster than $\sigma$, so $Z_{\text{eff}}$ increases — this drives the contraction in size and the rise in ionisation enthalpy, electron gain enthalpy, and electronegativity. Down a group, the increase in $Z$ is offset by a larger increase in $\sigma$ because new inner shells are filled, so $Z_{\text{eff}}$ increases only slightly or even decreases for the outermost electron — hence the atom expands and the other properties weaken.