Wave-like Properties of a Cadillac Passing Through a Freeway Underpass

In summary, the problem involves a Cadillac with a mass of 2000kg approaching a 10m wide freeway underpass. The question asks for the necessary speed and time for the car to have a wavelength that could potentially diffract after passing through the underpass, compared to normal freeway speeds of 30m/s. The solution involves using the de Broglie wavelength formula and setting it equal to the size of the underpass to find the required speed. The answers are 3.3*10^-38 m/s and 9.6*10^30 yr.
  • #1
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Homework Statement



A Cadillac with a mass of 2000kg approaches a freeway underpass that is 10m across. at what speed must the car be moving, and how long would it take to go the 10m, in order for it to have a wavelength such that it might somehow diffract after passing through this single "slit"? How do these conditions compare to normal freeway speeds of 30m/s?

Homework Equations



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The Attempt at a Solution



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well, I have no idea how to solve this question...
first of all, I cannot imagine what's going on here, partly because I'm not a native english speaker...

Can someone teach me the way to solve this, in detail?
the answers are 3.3*10^-38 m/s and 9.6*10^30 yr.
 
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  • #2
I really don't see the point of this exercise - but they want you to use the de Broglie wavelength=h/p (where p is the momentum). Just set wavelength roughly equal to the 'slit' size of 10m and figure out v. Then figure out how long it would take you to cross 10m at that velocity.
 
  • #3
ah-huh, i kind of understood the question now.
Thank you!
 

1. What is the wave-particle duality?

The wave-particle duality is the concept that matter can exhibit both wave-like and particle-like behavior. This means that matter, such as subatomic particles, can behave like waves with properties such as wavelength and frequency, but also have discrete properties like mass and momentum.

2. How does the double-slit experiment demonstrate the wave nature of matter?

The double-slit experiment is a classic experiment that demonstrates the wave nature of matter. In this experiment, a beam of particles, such as electrons, is directed at a barrier with two small slits. The particles passing through the slits form an interference pattern, similar to what would be expected from waves passing through two slits. This indicates that the particles have wave-like properties.

3. Can all types of matter exhibit wave-like behavior?

Yes, all types of matter, from subatomic particles to larger objects, can exhibit wave-like behavior. However, the degree to which this behavior is observable depends on the mass and velocity of the particle. The wave-like behavior becomes more prominent as the mass decreases and the velocity increases.

4. How does the uncertainty principle relate to the wave nature of matter?

The uncertainty principle, proposed by Werner Heisenberg, states that it is impossible to know both the position and momentum of a particle at the same time. This is because the act of measuring one of these properties affects the other. This principle is a fundamental aspect of quantum mechanics and is closely related to the wave-particle duality of matter.

5. What are some practical applications of understanding the wave nature of matter?

Understanding the wave nature of matter has led to many technological advancements, such as the development of electron microscopes, which use the wave-like behavior of electrons to view objects at a very small scale. It has also led to the development of technologies like transistors and lasers, which are essential in modern electronics. Additionally, this understanding has allowed scientists to manipulate matter at the quantum level, leading to advancements in fields like nanotechnology and quantum computing.

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