atomic radii

Meaning: An atom's electron cloud has no sharp edge, so its radius is measured indirectly, usually as half the internuclear distance in a bond between two identical atoms. Across a period, protons are added while electrons enter the same shell, so effective nuclear charge rises and pulls the cloud inward. Radius usually decreases left to right. Down a group, valence electrons sit in higher shells farther from the nucleus, and inner electrons shield them, so radius increases. Across the transition metals the change is usually small because added d electrons shield one another.

Equation: r ≈ d/2 and Zeff = Z − S, where r is atomic radius (m), d is the internuclear distance between two identical bonded atoms (m), Zeff is effective nuclear charge (in units of elementary charge), Z is the number of protons, and S is the shielding by inner electrons.

On the MCAT: Questions typically ask you to rank atoms or ions by size using periodic table position. Expect cations to be smaller than their parent atoms, anions larger, and isoelectronic series (for example O²⁻, F⁻, Na⁺, Mg²⁺) to shrink as the proton count rises.

Common confusion: Students assume more electrons means a larger atom. Across a period the shell stays the same and the added protons dominate, so the atom usually gets smaller. Down a group, the added shell is what makes it larger.