Lesson 2: Atomic radius

We study the trends of properties in the representative elements (s and p blocks).

2.1 Definition

• Because the wave theory shows it is impossible to fix the exact position of an electron, the atomic radius cannot be defined as "distance from the nucleus to the farthest electron".
• Instead:

Atomic radius (covalent radius) is half the distance between the centres of the nuclei of two identical atoms bonded in a diatomic molecule.

It is measured in picometres (pm); 1 pm = 10⁻¹² m. In ionic crystals (such as NaCl) the size of each cation or anion is described by its ionic radius, which depends on the number of electrons lost or gained.

Example: in a Cl₂ molecule the distance between the two nuclei is 198 pm, so the atomic radius of chlorine = 198/2 = 99 pm.

Atomic radii in pm:

2.2 Variation across a period (left to right)

The atomic radius decreases from group 1A to group 7A. Reason: the effective nuclear charge (Z_eff) increases gradually.

• Z_eff is the actual nuclear charge felt by an electron in the atom. It is always less than the real nuclear charge (number of protons) because the inner (core) electrons shield part of the nuclear attraction from the outer electrons.
• Across a period the number of protons increases by one at each step while the electrons are added to the same main level, so the shielding by inner electrons does not change much. Z_eff rises, the valence electrons are pulled closer, and the atom contracts.
• Hence the largest atom in a period is the alkali metal (1A) and the smallest is the halogen (7A).

Example: period 3: Na (186) > Mg (160) > Al (143) > Si (117) > P (110) > S (104) > Cl (99) pm.

2.3 Variation down a group

The atomic radius increases with atomic number. Reasons:

1. the number of energy levels increases;
2. the filled inner levels shield the outer electrons from the nucleus;
3. the repulsion between the electrons increases.

Example: group 1A: Li 152 < Na 186 < K 227 < Rb 247 < Cs 265 pm.

2.4 Ionic radius compared with atomic radius

• Metal cation is smaller than its atom (Na⁺ < Na; Fe²⁺ < Fe). Protons are the same but there are fewer electrons, so the effective nuclear charge per electron increases and the outer level is lost (for Na the 3s electron is removed). The larger the positive charge the smaller the ion (Fe³⁺ < Fe²⁺ < Fe).
• Non-metal anion is larger than its atom (Cl⁻ > Cl). The protons are the same but there is one more electron, so repulsion between electrons increases and the nuclear attraction per electron decreases (as in tug of war: the same pull shared by more electrons).