Can de Broglie wavelength of a particle be smaller than its size?
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Yes, that is possible. The momentum of the particle dictates its de-Broglie wavelength, not its dimension. Hence, large particles often have a smaller de-Broglie wavelength than their dimension. It has also been experimentally observed in this paper (more papers exist but this one deals with very large particles).

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A very common and well studied example is nuclear fusion of heavy ions. The de Broglie wavelength corresponds to the center of mass motion. – Apr 16 '18 at 12:53