[albutr]

Are you forgetting a Jacobian? The maximum probability isn't inside the nucleus for an s-orbital. E.g. for hydrogen, the maximum probability for the electron is one bohr radius away from the center of the nucleus (and the expectation value of the radius is 1.5 bohr radii away).

[Koshkin]

Well let me just quote Wikipedia here: ...in three-dimensional space, the maximum probability density occurs at the location of the nucleus and not at the Bohr radius, whereas the radial probability density peaks at the Bohr radius, i.e. when plotting the probability distribution in its radial dependency.

[BeetleB]

That it is maximum at the nucleus is not of much significance. To quote a professor:[1]

> In some ways it does not provide the best description of the electron distribution, since the region around r= 0, where the wavefunction has its largest values, is a relatively small fraction of the volume accessible to the electron. Larger radii represent larger physical regions since.

If you were to do any kinds of measurements, you are most likely to find it at the Bohr radius, not closer to the nucleus.

[1] http://www.umich.edu/~chem461/QMChap7.pdf

[albutr]

Ah yup you're right, I read your sentence too fast, whoops. The most likely location is at the nucleus, but the most likely radius (integrating over all angles) is at 1 bohr radius.