So my stupid question is: we know that in the classical model of a atom there is a nucleus at the middle and electron revolving around it in orbits numbered from 0 to infinity. So according to this an atom must have infinite space to accommodate infinite orbits. How is this possible and where am I going wrong?
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1$\begingroup$ This is unanswerable unless you define what you mean by "space that an atom occupies". Quantum physics, generally, has no precise notion of "occupied space". $\endgroup$– ACuriousMind ♦Commented Jun 9, 2015 at 15:00
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$\begingroup$ @ACuriousMind My knowledge about this subject is almost negligible as compared to you people.My question is purely out of curiosity. I think of an atom as a solid object which occupies a definite volume or space as I have often heard my teachers saying "Two atoms collide with each other ......" or "An atom breaks up into two particles ..... . $\endgroup$– Sourav KantaCommented Jun 9, 2015 at 15:09
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$\begingroup$ "Colliding" essentially means "interacting" and "breaking" means an interaction where one system splits into two which don't interact much afterwards. None of these needs notion of "size". Perhaps look also at this question where the notion of "solidity" for an atom is discussed. $\endgroup$– ACuriousMind ♦Commented Jun 9, 2015 at 15:17
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Even in the classical model, an infinite amount of levels doesn't necessarily mean that it occupies an infinite amount of space. You can divide any finite distance into infinitely many bits (for instance, $1 = \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \ldots$). EDIT: I'd forgotten about the $r\sim N^2$ relation that the OP mentions below, so yes, although the above is true, in the classical theory the size of the atom will go to infinity for $N\rightarrow\infty$.
However, the atom is not classical. Rather, the position of its electron is described by a probability density function which is non-zero at all distances even for the ground level, although it quickly reduces to zero-enough for most practical purposes. So your worry is still justified: In a sense, the atom does occupy all of the Universe.
Since in reality the atom is thus infinitely large, any practial definition of its size must be arbitrary, and indeed several definitions exist, which however are of the same order of magnitude, roughly an Ångström or so. From Wikipedia's article on the size of an atom: "Three widely used definitions of atomic radius are Van der Waals radius, ionic radius, and covalent radius."
