Mean radius of a circular Coulomb bound state
= Mean radius of a circular Coulomb bound state
For $R(r)\propto r^l e^{-r/[a(l+1)]}$, the radial probability density is proportional to $r^{2l+2}e^{-2r/[a(l+1)]}$ and
$$
\langle r\rangle=\frac{(2l+3)(l+1)}2a.
$$