De Broglie postulate and electron acceleration

AI Thread Summary
De Broglie's postulate establishes a relationship between a particle's momentum and its wavelength, expressed by the equation λ = h/p, indicating that matter exhibits both wave and particle characteristics. To investigate the atomic structure of a metallic surface using an electron beam, the electrons must be accelerated through a potential difference that converts electrical energy into kinetic energy. The kinetic energy of the electrons, given by 1/2 mv², can be equated to the work done by the potential difference, allowing for calculations of the required acceleration. The discussion emphasizes the importance of understanding electron momentum and energy in relation to atomic structure analysis. Overall, the principles of wave-particle duality and energy conversion are crucial for utilizing electron beams in material investigations.
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What relationship did de Broglie postulate between the momentum of a particle
and the wavelength of the corresponding matter wave?

Explain briefly how a beam of electrons may be used to investigate the atomic
structure of the surface of a metallic substance. Estimate the potential difference
through which the electron beam should be accelerated for this purpose, showing
your reasoning.
electron mass me = 9.11x10^-31 kg
electron charge e = 1.60x10^-19 C
Planck constant h = 6.63x10^-34 Js

Path difference: a(cosθi-cosθr)=nλ
Kmax=hv-W
E^2=p^2.c^2 + mo^2.c^4

Answer to question one surely is that matter can be described as both a wave and as a particle. The key equation would be: λ=h/p
For the second part, I'm trying to relate the potential difference to the velocity of the electron so I can find it's momentum, and then that can be used as the work on the electron.
 
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Well the potential difference would act up the electron's charge thus giving it kinetic energy, 1/2 mv2
 

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