In studying quantum mechanics, we find that all waves have object-like qualities

Question

In studying quantum mechanics, we find that all waves have object-like qualities and all objects have wave-like qualities. That technically means that all objects must obey the Heisenberg Uncertainy Principle. Let's assume the object is a 68 kg physics student and she moves through a 0.79 m wide door. We know that as she moves through the door, she must be somewhere inside its frame.

1) What is the uncertainty in her velocity? vstudnet = ___ m/sec

2) So it looks like we really won't care about the quantum mechanical effects involved unless we're worried about very, very small numbers. Another way of looking at the fact that all objects have wave-like properties is diffraction. Waves diffract as they move through a small opening and technically quantum mechanics means that all objects should diffract like a wave when going through a "slit". Again, let's assume the object is our 68 kg physics student and she moves through the "slit" of a 0.79 m wide door. We know that the diffraction of a wave first becomes significant when the width of the aperture is comparable to the wavelength of the waves being diffracted. At what speed should the student be moving in order to have signficant diffraction as she enters the door?

vstudnet = ___ m/sec

3) Lets assume she "enters" the room by moving 1 meter from the outside of the door to inside. At this speed, how long would it take for the student to enter to room? tenter = ___ years

Explanation / Answer

using heisenberg uncertainy principle

dx * m*dv = h / 4*pi

dv = h / 4*pi*m*dx

dv = 5.27*10^(-35) / 6*0.79

dv = 9.81*10^(-37) m/s

()

p = h / lambda

m*v = h / lambda

v =6.62*10^(-34) / 68*0.79

v = 1.23*10^(-35) m/s

(c)

t = x / v

t = 1 / 1.23*10^(-35)*3600s*24h*365.25d

t = 2.57*10^27 yrs

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