Radius with Bohr model
The hydrogen atom wavefunctions can be useful for multielectron atoms as a means of looking up their size (by means of a parameterization). The hydrogen atom wavefunctions form one possible basis for the definition of effective nuclear charges, see for instance here, where  Hartree–Fock orbitals are used to compute effective charges:

$$ Z_{eff} = \frac{&lt;r&gt;_H}{&lt;r&gt;_Z}$$

Here $&lt;r&gt;_H$ and $&lt;r&gt;_Z$ are the mean hydrogenic and Hartree-Fock radii (for nuclear charge Z).

The mean hydrogenic radius for ground state hydrogen is related to the Bohr radius $a_0$ as 
 $$&lt;r&gt;_H = \frac{3}{2}\frac{a_o}{Z}$$

Expressions for $&lt;r&gt;_H$ are available for other orbitals, allowing $&lt;r&gt;_Z$ to be computed from the tabulated values of $ Z_{eff}$ as

$$ &lt;r&gt;_Z = \frac{&lt;r&gt;_H}{Z_{eff}}$$

So using the hydrogen wavefunctions in this way is a little more complicated than using the equation for the Bohr model, but just the s-orbitals can already be useful to give you an idea about the size of atoms.