Wavelength of 1.5keV (kinetic energy) electron

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SUMMARY

The discussion focuses on calculating the wavelength of an electron with a kinetic energy of 1.5 keV. It establishes that this energy is significantly lower than the electron's rest energy of 511 keV, indicating that non-relativistic equations, such as 1/2mv^2, can be applied. However, the wavelength can be determined using momentum rather than velocity. The conversation also highlights the existence of both relativistic and non-relativistic formulas that relate energy, momentum, and mass.

PREREQUISITES
  • Understanding of kinetic energy and its relation to momentum
  • Familiarity with relativistic and non-relativistic physics concepts
  • Knowledge of the electron's rest energy (511 keV)
  • Basic mathematical skills for deriving formulas
NEXT STEPS
  • Study the relativistic energy-momentum relation formula
  • Learn how to derive the non-relativistic kinetic energy and momentum formulas
  • Explore the de Broglie wavelength equation for particles
  • Investigate the implications of relativistic effects on particle behavior
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Physics students, educators, and professionals interested in quantum mechanics and particle physics, particularly those focusing on electron behavior and wave-particle duality.

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How would one find the velocity of this electron. Is it considered relativistic or will 1/2mv^2 work just fine??
 
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I think most people would consider this to be non-relativistic. 1.5 keV is much less than the electron's rest-energy which is 511 keV. If you have a little time you can calculate it both ways and see for yourself how much (or rather, how little) difference it makes.

Actually, to find the wavelength (which is what you asked about in the thread title), you don't even need the velocity. What you really need is the momentum.

If you want to do it relativistically, there's a formula that connects energy, momentum and mass, without using the velocity... have you seen it?

There's also a non-relativistic formula connecting kinetic energy, momentum and mass, which you can easily derive by combining the usual formulas for KE and momentum.
 
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