Why is an electron cloud pictured with a fuzzy line?

Answer 1

"Cloud" ought to give you a clue.Very, very small objects simply do not behave the same way that objects on the scale we're used to do. When you look at a Bowling ball, it looks (and feels, and acts) like it has a hard edge that's well-defined.

Electrons aren't like that. We can't even say with certainty where an electron is; it behaves in some ways as if it's lots of places at once, and even when we can narrow it down to a smaller region, it can "jump" from that region to another one without ever seeming to pass through the space in between. The best we can do is talk in terms of probabilities, and while the probability for an electron in an atom is highest for the region near the nucleus of that atom (well, at least relatively near ... within an Angstrom or two), the probability that it's several feet ... or miles ... or light-years ... away is not zero (it's just very close to zero). So we can't draw a sharp line and say "the electron is definitely inside here". Given that, it makes more sense to depict the line as "fuzzy", which better conveys the idea "the electron is probably somewhere inside here ... we're about 90 (or 95, or 99) percent sure of it ... but it might be outside".