Periodicity - Periodic trends

Effective Nuclear Charge ($Z_{eff}$): The net positive charge experienced by valence electrons. It is calculated as $Z_{eff} = Z - S$, where $Z$ is the atomic number and $S$ is the number of shielding (inner) electrons. $Z_{eff}$ increases across a period but remains relatively constant down a group.

Atomic Radius: The distance from the nucleus to the outermost electron shell. It decreases across a period due to increasing $Z_{eff}$ pulling electrons closer, and increases down a group due to the addition of new principal energy levels ($n$).

Ionic Radius: Cations ($M^{n+}$) are always smaller than their parent atoms because the loss of electrons reduces repulsion and often removes an entire outer shell. Anions ($A^{n-}$) are always larger than their parent atoms because added electrons increase inter-electronic repulsion, expanding the electron cloud.

First Ionization Energy ($IE_1$): The energy required to remove one mole of electrons from one mole of gaseous atoms: $X(g) \rightarrow X^+(g) + e^-$. It increases across a period and decreases down a group, with notable exceptions at Group 13 (dropping from $s^2$ to $p^1$) and Group 16 (electron pairing repulsion).

Electronegativity: A dimensionless quantity (Pauling scale) representing the ability of an atom to attract a shared pair of electrons in a covalent bond. Fluorine ($F$) is the most electronegative element ($4.0$). It increases across a period and decreases down a group.

Electron Affinity ($E_{ea}$): The energy change when one mole of electrons is added to one mole of gaseous atoms: $X(g) + e^- \rightarrow X^-(g)$. Values generally become more exothermic (more negative) across a period as $Z_{eff}$ increases.

Metallic Character: The tendency of an element to lose electrons and form positive ions. It decreases across a period and increases down a group. Oxides of metals are generally basic (e.g., $Na_2O$, $MgO$), while oxides of non-metals are acidic (e.g., $P_4O_{10}$, $SO_3$).