Consider one of the doorways in our classroom. a) Approximately what de Broglie

Question

Consider one of the doorways in our classroom. a) Approximately what de Broglie wavelength should an object have in order to show noticeable diffraction effects when passing through this doorway? Explain your reasoning. b) Suppose one of our lab carts from Physics 101 is rolling through the door. Estimate what its speed should be in order to have the de Broglie wavelength you specified in part (a). How long would it take to pass through the doorway at this speed? Based on your result, explain why we would be unlikely to notice such quantum effects in a Physics 101 experiment.

Explanation / Answer

(a) For a particle to show diffraction, its de broglie wavelength should be comparable to the size of the slit/doorway, say 1 metre.

(b) p=h/wavelength.

p is momentum , h is planck constant.

p=mv.

As its mass would be ~1kg.

So, v=h/(m× wavelength)

v= h, so, velocity is of order of 10-34m/sec.

T =distance/speed.

So, time taken would be of the order of 1034seconds ~ forver to cross doorway.

Quantum effects are not seen as wavelength is very large.

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