# Chapter 28 - Problems - Page 1074: 3

(a) $v = 8.2\times 10^{-30}~m/s$ (b) $t = 1.5\times 10^{28}~s$

#### Work Step by Step

(a) To exhibit diffraction, the de Broglie wavelength should be equal to the width of the doorway. We can find the required speed: $\lambda = \frac{h}{mv}$ $v = \frac{h}{m~\lambda}$ $v = \frac{6.626\times 10^{-34}~J~s}{(1.0\times 10^{-4}~kg)(0.81~m)}$ $v = 8.2\times 10^{-30}~m/s$ (b) We can find the time to walk through the doorway: $t = \frac{d}{v}$ $t = \frac{0.12~m}{8.2\times 10^{-30}~m/s}$ $t = 1.5\times 10^{28}~s$

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