Example 3
An 81 -kg student who has just studied matter waves is concerned that he may be diffracted as he walks through a doorway that is $81 \mathrm{cm}$ across and $12 \mathrm{cm}$ thick. (a) If the wavelength of the student must be about the same size as the doorway to exhibit diffraction, what is the fastest the student can walk through the doorway to exhibit diffraction? (b) At this speed, how long would it take the student to walk through the doorway?