Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 28 - Quantum Mechanics of Atoms - General Problems - Page 828: 63

Answer

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Work Step by Step

The wavelength is about the same order of magnitude as the width of a typical doorway so yes, you would notice diffraction effects. We find your speed using equation 27–8. $$\lambda=\frac{h}{p}=\frac{h}{mv}$$ $$v =\frac{h }{m \lambda } $$ $$v =\frac{6.626\times10^{-34}J \cdot s }{(68.0kg) (0.50m)}=2.0\times10^{-35}m/s$$ The time required to pass through a doorway moving at that speed, assuming that traveling 0.25 m means you are “through” the doorway, is unimaginably long. $$\Delta t = \frac{L}{v}=\frac{0.25m}{2.0\times10^{-35}m/s }\approx 1.2\times10^{34}s\approx 4.1\times10^{26}\;years$$
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