The radius of the $n$th Bohr orbit in a hydrogen-like atom of nuclear charge $Z$ scales as

Equating the Coulomb force $\tfrac{kZe^2}{r^2}$ with the centripetal demand and substituting Bohr's quantisation $mvr = n\hbar$ gives $r_n = \tfrac{n^2 \hbar^2}{m k Z e^2}$, i.e. $r_n \propto \tfrac{n^2}{Z}$. Energy scales the opposite way: $E_n \propto -\tfrac{Z^2}{n^2}$.