The Schrodinger wave equation for hydrogen atom is
`psi _(2r)^(2)=0=[(1)/(4 sqrt(2 pi))]^(2) (2-(r_(0))/(a_(0)))e^(-r_(n)//a_(0))`
where `a_(0)` is Bohr's radius. Let the radial node be at `r_(0)` then find r in terms of `a_(0)`.

Explanation

At nodal point, `psi = 0`. From the given wave function, `psi =0` at the following values of r:
`[27-18((r)/(a_(0)))+2((r)/(a_(0)))^(3)]=0`
Solving for `r_(0)//a_(0)`, we get `r_(0)//a_(0)=((r_(0))/(a_(0)))=(18 pm sqrt(18^(2)-216))/(4)=(18 pm 10.4)/(2)`
There is a node at `r= prop`