De Broglie wavelength of an ant

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Homework Help Overview

The discussion revolves around the de Broglie wavelength of an ant, specifically examining the conditions under which the ant might exhibit wave behavior as it passes through a hole in a screen. The problem involves concepts from quantum mechanics and wave-particle duality.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationship between the wavelength of the ant and the diameter of the hole, questioning whether the wavelength should be comparable to the hole's size. There is also a discussion about the amplitude of the wave and its relevance to diffraction.

Discussion Status

The conversation is ongoing, with participants sharing their thoughts on the relationship between wavelength and hole size. Some guidance has been offered regarding the wavelength being of the order of the hole's diameter, but questions remain about the implications of amplitude and diffraction.

Contextual Notes

Participants are considering the physical parameters of the ant, including its mass and the dimensions of the hole, while also grappling with the conceptual aspects of wave behavior in this context.

DunceMoin
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An ant of mass m = 1.80×10−6 kg goes through a hole of diameter D = 5.00 mm in a window screen which has thickness L = 0.600 mm.

(a) What should be the approximate wavelength and speed of the ant for it to show wave behavior as it goes through the hole?

I am not sure what should the approximate wavelength be. Should it be of the order of the diameter of hole? If not, what's the concept involved? Also, once we have wavelength, the speed should be very simple to calculate from de Broglie's formula.
 
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Hello and welcome to PF!

I think you have the right idea: the wavelength should be of the order of the diameter of the hole.
 
TSny said:
wavelength should be of the order of the diameter of the hole
Shouldn't amplitude be of the order of the radius? just asking.
 
Suraj M said:
Shouldn't amplitude be of the order of the radius? just asking.
I don't believe so. The amplitude of a wave does not have a direct effect on the amount of diffraction.
 

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