Diffraction effects become significant when the width of an aperture is comparable to the wavelength of the waves being diffracted. (a) at what speed will the de broglie wavelength of a 65-kg student be equal to the 0.76-m width of a doorway? (b) at this speed, how much time will it take the student to travel a distance of 1.0 mm? (for comparison, the age of the universe is approximately 4 * 1017 s.)

To develop this problem it is necessary to apply the concepts related to Broglie hypothesis.

The hypothesis defines that

Where,

P = momentum

h = Planck's constant

The momentum is also defined as,

P = mv

Where,

m = mass

v = Velocity

PART A) Replacing at the first equation

Our values are given as,

Re-arrange to find v, we have:

PART B) From the kinematic equations of movement description we know that velocity is defined as displacement over a period of time, that is

Re-arrange to find t,

the age of the universe.