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Exercise · Q15

Q.Explain, using de Broglie's own reasoning, why the wave nature of matter is never observed for everyday moving objects such as a thrown ball or a moving car, even though the de Broglie relation applies, in principle, to every moving object.

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The formula and what it depends on. De Broglie's relation λ=h/mv\lambda=h/mv makes the wavelength INVERSELY proportional to the particle's momentum mvmv. It applies to every moving object, in principle, but hh itself (6.63×10−34 J s6.63\times10^{-34}\ \text{J s}) is an extraordinarily small constant.

Everyday objects. For a macroscopic object -- even something as light as a table-tennis ball, moving at an ordinary speed -- the momentum mvmv, expressed in ordinary SI units, is already many, many orders of magnitude LARGER than hh itself, so dividing hh by it gives a de Broglie wavelength many orders of magnitude smaller than the diameter of a single atomic nucleus (Numerical 6 works through an explicit case). No experiment, and no physical process, can detect or is affected by a wavelength that small, so the object's motion appears purely particle-like, with no observable wave character at all. …

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