Is the Electron Confined to a Fixed Radius in Hydrogen's Ground State?

[jaejoon89]

I was wondering if the following responses, and their line of reasoning, is correct:

The wavefunction is 0 at the nucleus for each stationary state of the hydrogen atom.
-> False (thinking in terms of the radial distribution, it only approaches 0)

The most probable value of the electron-nuclear distance in the ground state hydrogen atom is 0.
-> True (symmetric about nucleus)

For hydrgen in the ground state, the electron is confined to move w/in a sphere of fixed radius.
-> True (in ground state: 1s)

 

[gabbagabbahey]

The most probable value of the electron-nuclear distance in the ground state hydrogen atom is 0.
-> True (symmetric about nucleus)

The most probable distance is the same as the expectation of the radial operator, correct?

So, you are basically saying that $\langle\hat{r}\rangle=0$ for an electron in the ground state of Hydrogen. Does the fact that the ground state wavefunction is spherically symmetric really support this claim?

For hydrgen in the ground state, the electron is confined to move w/in a sphere of fixed radius.
-> True (in ground state: 1s)

How does the fact that the ground state is the 1s orbital support your claim?,,,What is the wavefunction of the groundstate? Is it zero for all values of $r$ except for some fixed radius, say $r_0$?...If not, then isn't it possible to find (measure the position of) the electron at more than one radius?