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A glass breaks when a sound wave matches the frequency produced by glass when it vibrates. Can we use this phenomenon of resonance to split an atom?

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There is one inherent flaw to this idea which is that sound waves need atoms to propagate. This also means that there is a limit to the size of the wavelengths of the waves which is set by the "granularity" of the medium.

So the sound wave can't actually reach a scale where it is able to induce resonance in an atom. Furthermore the frequencies required to make the wavelength small enough are ridiculously high. So high in fact that they are limited by properties of the medium. Even at 1GHz the sound wave would only have a wavelength of $3*10^{-4}$m which is still 6 orders of magnitude away from the size of a hydrogen atom.

Even then We haven't considered quantum mechanics and the fact that the electrons and the nucleus will only interact through photon exchange or the weak interaction.

So in short, no we cannot shake apart an atom using sound waves and the principle of resonance.

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I would answer this question with a "probably not", as sonoluminescence is an active field of research, and there have been dubious claims of nuclear fusion in the process. The phenomenon involves sound generated bubbles in fluids. The collapsing bubbles producing surprisingly high temperatures (certainly thousands of degrees K, with claims in the millions). While there may not be nuclear reactions, there is ionization. See https://en.wikipedia.org/wiki/Sonoluminescence for more.

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