the atomic radius
How big is an atom? The question is trickier than it sounds, because an atom has no hard edge; its electron cloud just fades away. So we cheat pragmatically: we say the atomic radius is half the distance between the centres of two identical atoms that are bonded together. Treat each atom as a soft sphere; the radius is the size that makes those spheres just touch at the measured bond length.
Atomic radii run from about 0.5 to 2.5 angstrom (0.05 to 0.25 nm). They follow clear periodic-table trends: radius grows down a group (more shells stacked outward) and shrinks across a period from left to right (the growing nuclear charge pulls the same shell in tighter). So a caesium atom (about 2.6 angstrom) is huge next to a fluorine atom (about 0.5 angstrom). The exact number also depends on how the atom is bonded, so we distinguish a metallic radius, a covalent radius, and (for charged atoms) an ionic radius; the same atom looks a little different in different company.
Size governs which structures are even possible. In close-packed metals, atoms behave like stacked equal spheres, and the packing that results (74 percent filled) is a direct consequence of treating atoms as hard balls. Size differences decide whether one atom can substitute for another in an alloy (similar sizes mix easily) or squeeze into the gaps between atoms (a much smaller atom fits interstitially, like carbon in iron to make steel). Radius is the ruler behind the whole geometry of crystals.
Carbon atoms are small (radius about 0.77 angstrom), so carbon can tuck into the octahedral gaps of an iron lattice (iron radius about 1.24 angstrom) as an interstitial, the basis of steel. If carbon were as large as iron it could not fit, and steel as we know it would not exist.
Atomic radius is the effective size that sets bond lengths and which structures fit.
There is no unique true atomic radius; the number depends on the bonding type and the definition used, and can vary by 10 percent or more between tables. Always check whether a quoted radius is metallic, covalent, or ionic before comparing values.