After learning about de Broglie\'s hypothesis that particles of momentum p have

Question

After learning about de Broglie's hypothesis that particles of momentum p have wave characteristics with wavelength lambda = h/p, an 70.3kg student has grown concerned about being diffracted when passing through a 70.8cm wide doorway. Assume that significant diffraction occurs when the width of the diffraction aperture is less than 10.0 times the wavelength of the wave being diffracted.

1) Determine the maximum speed at which the student can pass through the doorway in order to be significantly diffracted.

2) With that speed, how long will it take the student to pass through the doorway if it is 10.2cm thick?

Explanation / Answer

The wavelength of the student is

lambda = h/mv

If w is the width of the diffracting aperture

then we need

w < 10*lambda

w < 10*h/mv

So

v < 10*h/mw

v < 10*6.626*10^-34/(70.3*70.8*10^-2)

v < 1.33*10^-34 m/sec

B. using

distance = velocity*time

time > d/v

time > 0.102/(1.33*10^-34)

time > 7.67*10^+32 sec

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