Formula sheet: Classification of Elements and Periodicity in Properties

1.1 The law behind the table

The modern periodic law uses the proton count as the ordering quantity. Element properties come back in a regular pattern as that count increases. The repetition is not a property of the numbers themselves; it follows because the outer electronic configuration returns to a similar arrangement after every noble gas.

1.2 Position from configuration

The period number equals the highest principal quantum number occupied by electrons. The group number follows from the outer configuration: elements whose last electron enters an s orbital belong to group 1 or 2, those in p orbitals fall in groups 13 to 18, and d and f block elements sit in the transition and inner transition series. The number of valence electrons and the block together decide the group.

The screening order of the subshells in a shell is s greater than p greater than d greater than f, so an outer s electron is shielded least and held most tightly. A larger effective nuclear charge pulls the electron cloud inwards, which is the single idea behind most of the trends below.

1.3 Atomic and ionic radii

Atomic radius is measured as half the distance between the centres of two bonded atoms, so a covalent radius, a metallic radius and a van der Waals radius are not the same number. Down a group the radius increases because a new shell is added. Across a period the radius decreases because the nuclear charge grows while the electrons stay in the same shell.

Ions follow short rules. Losing electrons gives a smaller species, because fewer electrons are pulled in by an unchanged nuclear charge. Gaining electrons gives a larger species, because the extra charge raises electron-electron repulsion. In an isoelectronic set, the species carrying the most protons is the most compact.

1.4 Ionization enthalpy

The first ionization enthalpy is the energy needed to remove the most loosely bound electron from an isolated gaseous atom in its ground state. The state is written in the definition because only an isolated atom and only the ground state give values that can be compared.

Successive ionization enthalpies grow because the remaining electrons are held by a positive ion. A large jump between two successive values reveals that the next electron comes from an inner shell. Down a group the first ionization enthalpy falls as size grows and shielding increases. Across a period it generally rises with the effective nuclear charge, with dips at the filled and half-filled configurations.

1.5 Electron gain enthalpy and electronegativity

Electron gain enthalpy measures the enthalpy change that accompanies the addition of one electron to an isolated atom in the gas phase. A negative value means energy is released, so the more negative the value, the stronger the tendency to accept an electron. Chlorine has a more negative value than fluorine because fluorine's compact 2p subshell repels the incoming electron. Noble gases have positive values.

Electronegativity is not an energy. It is the tendency of an atom in a molecule to attract the shared electron pair towards itself. The Pauling scale runs from fluorine at 4.0 downwards, and it rises across a period and falls down a group.

1.6 Trends at a glance