If you could keep utterly motionless, your de Broglie wavelengthwould be infinite. As soon as you make the slightest motion,however, your wavelength collapses. (a) Estimate the lowest speed youcan perceive. (b) Estimate your wavelength if you moved with that slowestperceptible speed. (c) A grain of sand has a mass of about 0.5 mg.Estimate the wavelength of a grain of sand moving at your slowest perceptiblespeed. (It should be clear that the wave aspects of macroscopicmaterial things are hidden from us by our size.) (d) If nature were to alterher laws so that Planck’s constant became h = 1 J . s, then what wouldbe the wavelength of a grain of sand moving at 1 m/s? (e) Under thesesame circumstances, estimate your own wavelength if you ran at 2.5 m>s.(f) A baseball has a mass of 145 g. Estimate the speed that a baseballwould need to have a perceptible diffraction, meaning a central maximumsubtending 10 , when thrown through a doorway, if h were 1 J . s.
If you could keep utterly motionless, your de Broglie wavelength
would be infinite. As soon as you make the slightest motion,
however, your wavelength collapses. (a) Estimate the lowest speed you
can perceive. (b) Estimate your wavelength if you moved with that slowest
perceptible speed. (c) A grain of sand has a mass of about 0.5 mg.
Estimate the wavelength of a grain of sand moving at your slowest perceptible
speed. (It should be clear that the wave aspects of macroscopic
material things are hidden from us by our size.) (d) If nature were to alter
her laws so that Planck’s constant became h = 1 J . s, then what would
be the wavelength of a grain of sand moving at 1 m/s? (e) Under these
same circumstances, estimate your own wavelength if you ran at 2.5 m>s.
(f) A baseball has a mass of 145 g. Estimate the speed that a baseball
would need to have a perceptible diffraction, meaning a central maximum
subtending 10 , when thrown through a doorway, if h were 1 J . s.
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