This is not an easy question to answer. First, note that it’s a bit dicey to talk about electrons bound to a nucleus as occupying any definite place in space, or following definite orbits as in the familiar ‘solar system’ (Bohr) model of the atom. Rather, all that you can really say is that at a certain point in space, there is a certain probability to observe the electron there, if you look. These probabilities are given by the orbitals of the atom – you’ve probably seen funny pictures like this one before. What they tell you is the shape of the probability distribution (more accurately, the wave function; the probability is obtained by integrating over the absolute square of the wave function); at any point on their surfaces, the electron is equally likely to be found. Radially, i.e. at some distance from the atom, these go like r*exp(-r) in the simplest case (see here). As you can see, this never reaches 0 – there is always a non-vanishing probability to observe an electron at any distance from its atom (the probability gets really small really quick, though). The typical distance is around the Bohr radius, in the vicinity of half an Angström (10[sup]-10[/sup]m).

Now, you have on the order of 10[sup]28[/sup] atoms in your body. The likelihood of observing an electron in an interval between 35 and 36 times the Bohr radius away from its nucleus is ~10[sup]-28[/sup]. So, if you measured all your atoms at that distance, there’s a good chance you’d find an electron there at least once (and perhaps a couple of times; this is such a quick and dirty calculation that I’d be happy to be correct within an order of magnitude or two). This would translate to something around 2 nm, perhaps.

Of course, this calculation is heavily approximated. First of all, I’ve essentially assumed that you’re composed entirely out of hydrogen, and second, that all of your atoms are in the ground state, neither of which will be true. In particular, excited atoms can have a much larger radius – the radius scales with n², where n is the excitation level of the atom; you can produce extremely large atoms, so-called Rydberg atoms, which can have radii in the range of micrometres. I’ve also treated your atoms as a collection of systems in isolation, which is probably not a good approximation, so it’s dubious whether the quantum-mechanical calculation is really applicable at all.

So in short, yeah, it’s not an easy question to answer…