De Broglie Wavelength of Electron

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SUMMARY

The discussion focuses on calculating the de Broglie wavelength of an electron with varying kinetic energies: 50.0 eV, 50.0 keV, and 3.00 eV. Participants clarify the use of the equations E=hf and 1/2 m(v^2) to derive the wavelength from kinetic energy. The relationship between momentum and wavelength is established using the formula λ = h/p, where p is derived from kinetic energy. The conversation emphasizes the wave-particle duality of electrons, confirming that both particle and wave properties can be considered simultaneously in calculations.

PREREQUISITES
  • Understanding of kinetic energy equations, specifically 1/2 m(v^2)
  • Familiarity with Planck's constant and its application in quantum mechanics
  • Knowledge of the de Broglie wavelength formula λ = h/p
  • Basic concepts of wave-particle duality in quantum physics
NEXT STEPS
  • Calculate de Broglie wavelengths for various particles using their kinetic energies
  • Explore the implications of wave-particle duality in quantum mechanics
  • Learn about the relationship between energy and frequency using E=hf
  • Investigate the applications of de Broglie wavelength in modern physics
USEFUL FOR

Students of quantum mechanics, physics educators, and anyone interested in the principles of wave-particle duality and the behavior of electrons in various energy states.

amcca064
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Homework Statement


Ok, question is: " Calculate the de Broglie wavelength for an electron that has kinetic energy a)50.0 eV b) 50.0 keV and c) 3.00 eV d) What If? A photon has energy 3.00 eV. Find its wavelength.

Homework Equations



E=hf

1/2 m(v^2)

*lambda* = Planck's constant / momentum

The Attempt at a Solution



Was just going to use E = hf then find wavelength from f, but realized that v is unknown unless I can use classical equation K=1/2m(v^2) but I was not sure I can do this? If I can, problem is easy, if I can't... will need some help... Thanks!
 
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You have the energy, what do you want to find v for? Use the Planck's constant with eV in it, and your units should work out.
 
Are you familiar with the De Broglie relationship, or are you studying in advance? ;-)

You need to use the final 2 equations you stated.

From E=1/2 * m * v^2

2E = m v^2
2Em = (m v)^2
2Em = p^2 p=momentum
p = (2Em) ^ 0.5
h/lambda = (2Em) ^0.5

Should be easy to find wavelength with the above equation.
 
mindscrape - don't need v, need v to find p, or at leaast i thought i needed it until I see that I can do what QuantumCrash suggests...

Was not sure if I could use de Broglie wavelength equation WITH Kinetic energy of a particle equation. i.e. Wasn't sure if i could consider electron particle AND wave in the same situationi. I thought maybe had to consider electron only as wave or only as particle depending on situation. But now I see can do both, Thanks for the help!
 
hahaha just realized that this is what de Broglie wavelength is all about anyways! wave-particle duality. wow, funny
 

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