The classical image of an atom is inaccurate.
Can you give me a better mental image of an atom, an electron?
Let us concentrate on the simplest atom, the hydrogen atom
(one proton with 1 electron nearby). In order to
visualize the H atom, first we have to specify its energy
state. If we specify that the atom is in its lowest
energy state, then there is a well-defined probability
of finding the electron at some distance r from the
proton. The probability is "spherically symmetric" about
the proton, i.e., all points on a sphere of any radius centered
at the proton will have the same "probability density."
But what is the radial dependence of the probability? Well,
one usually looks at the "radial distribution function,"
which is the probability of finding the electron within a
spherical shell of tiny (infinitesimal) thickness centered on the
nucleus. For the atom in its lowest energy state, this looks
like a snail with its head at r=0, a hump in the middle,
and a long tail which reaches out to r = infinity. The r where
the hump is is the "most probable" distance of the electron
from the nucleus. However, this is not the same as the average distance
(which you get by integrating the r.d.f. from 0 to infinity).
In short; the H atom in its ground state has a spherically symmetric
probability function, and there is a finite probability of "finding"
an electron at any distance r from the nucleus.
The excited states are more interesting, and would take too long to
answer in this small space. But I hope this piques your interest...
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Update: June 2012