Answer
(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:
$t = \frac{d}{v}$
$t = \frac{0.12~m}{8.2\times 10^{-30}~m/s}$
$t = 1.5\times 10^{28}~s$
