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 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.

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Learning Goal: To understand de Broglie waves and the calculation of wave properties. In 1924, Louis de Broglie postulated that particles such as electrons and protons might exhibit wavelike properties. His thinking was guided by the notion that light has both wave and particle characteristics, so he postulated that particles such as electrons and protons would obey the same wavelength-momentum relation as that obeyed by light: \ =h/p, where X is the wavelength, p the momentum, and h Planck's constant. X = 1.06×10-34 Submit Correct m Previous Answers -14 As a comparison, an atomic nucleus has a diameter of around 10 m. Clearly, the wavelength of a moving baseball is too small for you to hope to see diffraction or interference effects during a baseball game. Part C Consider a beam of electrons in a vacuum, passing through a very narrow slit of width 2.00 μm. The electrons then head toward an array of detectors a distance 0.9540 m away. These detectors indicate a diffraction pattern,…
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