Work out atomic radius trend instantly with clear inputs, formula shown and shareable results.
The hydrogenic radius scales as n squared over the effective nuclear charge, with the Bohr radius (52.92 pm) setting the scale. Slater's rules give the effective charge as Z minus a shielding constant. Sodium, with n = 3, Z = 11 and S near 8.8, comes out around 215 pm - which explains both trends at once: radius grows down a group as n rises, and shrinks across a period as effective charge rises faster than shielding.
Effective nuclear charge
Zeff = Z - S
Hydrogenic radius
r = n^2 x a0 / Zeff, with a0 = 52.9177 pm
Each added proton pulls harder, but the added electron shields only partly, so effective charge rises and the shell contracts.
It captures the trends but not the absolute values, typically within 20-30% of measured covalent radii. Use it for comparison, not for bond lengths.