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Not sure what you mean by "Collapsing Atom Paradox," but I'll explain what I THINK you're asking about.
If the popular view of the atom -- electrons circling a nucleus like planets around a star -- were the correct view, the electrons would give off electro-magnetic energy (due to their acceleration) so rapidly that their orbit would decay in less than a billionth of a second. The quantum mechanics that rules our Universe makes this impossible, but it also destroys the popular view I noted earlier. Electrons are NOT circling a nucleus; indeed, it is meaningless to speak of what they actually ARE doing. Instead, electrons are in energy states -- called "orbitals" -- around a nucleus. Different orbitals have different probabilities for the locations of the electrons depending on radius and angle. However, it is NOT correct to think of the electrons as moving in an orbit.
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BlakeQuantum mechanics resolves the collapsing atom paradox by introducing the concept of superposition, where particles can exist in multiple states simultaneously until measured, and the wave function collapse occurs upon measurement. This means that an atom can exist in multiple states until an observation is made, at which point it assumes a definite state. This phenomenon is fundamental to the probabilistic nature of quantum mechanics.
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