The radial wave equation for hydrogen of radial nodes from nucleus are:
`Psi_(1s)=(1)/(16sqrt(4))(1/a_(0))^(3//2) [("x"-1)("x"^(2)-8"x"+12)]e^(-x//2)`
where, `x=2r//a_(0),a_(0)` = radius of first Bohr orbit
The minimum and maximum position of radial nodes from nucleus are:

Explanation

`Psi = (1)/(16 sqrtpi) ((1)/(a_(0))^(3//2)) [(x -1) (x^(2) -8x - 12)] e^(-x//2)`
At radial node, `Psi = 0`. Hence, `(x -1) = 0 or (x^(2) -8x - 12) = 0`
If `x -1 = 0`, then `x = 1`, i.e., `(2r)/(a_(0)) = 1 or r = (a_(0))/(2)`
If `x^(2) -8x + 12 = 0`, i.e.,` (x -6) (x -2) = 0`, then `(x -6) = 0 or (x -2) = 0`
If `(x -2) = 0`, then `x = 2 or (2r)/(a_(0)) = 2 or r = a_(0)`
If `(x - 6) = 0`, then x = 6 or `(2r)/(a_(0)) = 6 or r = 3 a_(0)`
Thus, nodes exist at `(a_(0))/(2), a_(0) and 3a_(0)`. Minimum is at `(a_(0))/(2)` and maximum at `3a_(0)`