After learning about de Broglie's hypothesis that material particles of momentum p move as waves with wavelength = h/p, an 80.0-kg student has grown concerned about being diffracted when passing through a 75.0-cmwide doorway. Assume significant diffraction occurs when the width of the diffraction aperture is less that 10.0 times the wavelength of the wave being diffracted. (a) Determine the maximum speed at which the student can pass through the doorway if he is to be significantly diffracted. (b) With that speed, over what time interval does the student pass through the doorway if it is in a wall 15.0 cm thick? State how your answer compares with the age of the Universe, which is about 4 x 10¹7 s.

After learning about de Broglie's hypothesis that material particles of momentum p move as waves with wavelength = h/p, an 80.0-kg student has grown concerned about being diffracted when passing through a 75.0-cmwide doorway. Assume significant diffraction occurs when the width of the diffraction aperture is less that 10.0 times the wavelength of the wave being diffracted. (a) Determine the maximum speed at which the student can pass through the doorway if he is to be significantly diffracted. (b) With that speed, over what time interval does the student pass through the doorway if it is in a wall 15.0 cm thick? State how your answer compares with the age of the Universe, which is about 4 x 10¹7 s.