Can an electron in an s-orbital exist at the nucleus (r=0)?

[Steven Hanna]

My quantum textbook says that the probability of finding an electron in a 1s orbital between r and r+dr is given by Prob = (4/a^3)*(r^2)*exp(-2r/a) dr. In this case, Prob(0) = 0 because of the r^2, which is part of the volume element in spherical polar. Does this mean that it is impossible to find an electron at r = 0? I have learned the opposite in several chemistry classes, so I would very much appreciate if someone could clear this up.
Thanks!

 

[Vanadium 50]

The volume element at r = exactly zero is 0. The nucleus is somewhat bigger than that, and its volume element is non-zero, and therefore so is the probability.

 

[Steven Hanna]

The volume element at r = exactly zero is 0. The nucleus is somewhat bigger than that, and its volume element is non-zero, and therefore so is the probability.

Ah of course. Thank you!