Double-slit Interference for Photons and Electrons

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In summary, the question is asking for the kinetic energy of electrons in a double-slit interference experiment, given that the spacing between maxima is the same for both photons and electrons. To solve this, we need to equate the de Broglie wavelength of photons (lambda(p) = hc/Ey) and electrons (lambda(e) = h/(2mEe)^1/2) and solve for Ee, the kinetic energy of electrons, in terms of Eγ, me, and c. This can be done by equating the expressions for lambda(p) and lambda(e) and solving for Ee.
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dcramps
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Homework Statement


A double-slit interference experiment is performed with photons of energy Eγ. The same pair of slits is then used for an experiment with electrons. What is the kinetic energy of the electrons if the interference pattern is the same as for the photons (that is, the spacing between maxima is the same)? Express your answer in terms of Eγ, me (electron mass), and c (speed of light).

Homework Equations



The Attempt at a Solution


I really hate to do this, but I have absolutely no idea what it is asking me here or how to do it.

How does using photons and electrons change the outcome? I am unsure how to calculate the kinetic energy...do I modify the dsinΘ=mλ equation somehow?

I am really lost here!
 
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  • #2
Energy of photon = hc/lambda. hence lambda(p) = hc/Ey
For electrons lambda(e) = h/mv = h/(2mEe)^1/2
Equate lambda(p) and lambda(e) and solve for Ee
 
  • #3
For electrons, that's the de Broglie wavelength, correct? I had just happened across that in my notes, but didn't get so far as to change momentum to (2mEe)1/2

Thank you for responding at such a late hour >_< I was not expecting such a quick reply!
 

FAQ: Double-slit Interference for Photons and Electrons

What is the double-slit experiment?

The double-slit experiment is a classic physics experiment that demonstrates the wave-particle duality of light and matter. It involves shining a beam of particles or waves through a barrier with two small slits, and observing the resulting interference pattern on a screen.

What is the significance of the double-slit experiment?

The double-slit experiment has significant implications for our understanding of the nature of light and matter. It shows that particles can exhibit wave-like behavior, and vice versa, challenging our traditional understanding of the universe and paving the way for quantum mechanics.

How does kinetic energy relate to the double-slit experiment?

Kinetic energy is the energy an object possesses due to its motion. In the double-slit experiment, the kinetic energy of the particles or waves is what allows them to pass through the slits and create an interference pattern on the screen.

Can the double-slit experiment be performed with any type of particle or wave?

Yes, the double-slit experiment can be performed with any type of particle or wave, as long as it has enough energy to pass through the slits and create an interference pattern. This includes electrons, photons, and even larger particles like buckyballs.

What practical applications does the double-slit experiment have?

The double-slit experiment has numerous practical applications, including in the development of new technologies such as electron microscopes and particle accelerators. It also has implications for quantum computing and cryptography.

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