Electron vs Photon question? Significance of momentum?

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SUMMARY

The discussion centers on the comparison between electrons and photons in terms of wavelength and momentum, particularly in the context of electron microscopy versus optical microscopy. It is established that when an electron and a photon possess the same energy, the electron has a shorter wavelength and larger momentum, making it advantageous for high-resolution imaging. The significance of the electron's larger momentum lies in its ability to produce clearer images at atomic scales, as optical microscopes cannot resolve features smaller than their wavelength, which is typically in the range of 400-700 nm, compared to the sub-nanometer wavelengths achievable with electron microscopy.

PREREQUISITES
  • Understanding of de Broglie wavelength and momentum relationship (p = h/λ)
  • Familiarity with electron microscopy principles and applications
  • Knowledge of photon energy and its implications in imaging techniques
  • Basic grasp of wave-particle duality in quantum mechanics
NEXT STEPS
  • Research the principles of high-resolution transmission electron microscopy (HRTEM)
  • Study the implications of momentum in quantum mechanics and its applications
  • Explore the limitations of optical microscopy and advancements in imaging technologies
  • Learn about the role of gamma rays in imaging and their comparison to electron microscopy
USEFUL FOR

Students, researchers, and professionals in physics, materials science, and microscopy who seek to understand the advantages of electron microscopy over traditional optical methods, particularly in high-resolution imaging applications.

  • #31
curiousmind04 said:
Do the mirrors have a reflective index that tends towards one with increasing frequency?
Mirrors are made with highly reflecting materials, usually from metals, like gold or aluminium. Metals have high refractive index and high absorption, both changing with frequency, and above some frequency, they do not behave like metals any more.
 
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  • #32
comparing wavelengths is one issue and comparing energies and momenta is another. comparison works fine for altogether different systems such as optical and electron microscopy instruments because mathematics is simpler and equivalent. Photons will not work in electron microscopy and electrons will not work in optical microscopy instruments.

Coming to the second issue, momentum and energy of two particles in non relativistic case and for particles with non-zero rest mass is simply:
P = √2mE and [E = (p^2)/2m]. The first equation tells us that the momentum of the heavier of the two particles having equal energy will be larger. and second equation tells us that the the energy of the heavier particle of the particles with same momentum will be smaller. I think such a comparison should not be made between photon and an electron.
 

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