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

AI Thread Summary
To determine the speed required for a Cadillac to diffract through a 10m underpass, the de Broglie wavelength formula (λ = h/p) is applied, where p is momentum. The calculated speed is approximately 3.3 x 10^-38 m/s, leading to an extraordinarily long crossing time of about 9.6 x 10^30 years. This speed is vastly slower than typical freeway speeds of 30 m/s, highlighting the impracticality of the scenario. The exercise emphasizes the concept of wave-like properties of matter, particularly in relation to large objects like cars. Understanding these calculations illustrates the differences between classical and quantum mechanics.
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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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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.
 
ah-huh, i kind of understood the question now.
Thank you!
 

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