Minumum electron energy and microscopes

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SUMMARY

The discussion focuses on calculating the minimum electron energy required to resolve an atom's dimensions using an electron microscope. The key equations involved are E = hc/λ for photons and λ = h/p for electrons, with momentum defined as p=sqrt(2mK). The user initially misapplied the photon energy equation, leading to an incorrect result of 1.24e6 eV. The correct approach involves using the DeBroglie wavelength equation in conjunction with the kinetic energy formula for electrons.

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  • Understanding of electron microscopy principles
  • Familiarity with the DeBroglie wavelength concept
  • Knowledge of kinetic energy and momentum relationships
  • Basic grasp of quantum mechanics equations
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  • Learn about the principles of electron microscopy and its applications
  • Explore the Compton shift and its implications in particle physics
  • Investigate advanced topics in quantum mechanics related to wave-particle duality
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Students in physics, particularly those studying quantum mechanics and microscopy, as well as researchers interested in atomic-scale imaging techniques.

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Homework Statement



The highest achievable resolving power of a microscope is limited only by the wavelength used; that is, the smallest item that can be distinguished has dimensions about equal to the wavelength. Suppose one wishes to "see" inside an atom. Assuming the atom to have a diameter of 100 pm, this means that one must be able to resolve a width of, say, 10 pm.

(a) If an electron microscope is used, what minimum electron energy is required?

Homework Equations



E = hc/λ
λ = h/p (DeBroglie wavelength)
p=sqrt(2mK) Momentum
Δλ = (h(1-cos θ))/mc Compton Shift

The Attempt at a Solution


I tried the equation E = hc/λ = (6.63e-34)(3e8)/(1e-12) = 1.24e6 eV, but that isn't the answer.
 
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E = hc/λ is for photons, not for electrons. What's the equation that gives an object's kinetic energy in terms of its momentum?
 
p=sqrt(2mK)

So, do I use that equation in conjunction with DeBroglie's? λ = h/p This one is used for electrons, right?
 

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