Electron Microscope Resolution Limit · AI Generator #GEN-9FD4C5C7

Physics · modern-physics

Problem

A modern transmission electron microscope (TEM) accelerates electrons from rest through a potential difference of 120  kV120\;\text{kV} to achieve high-resolution imaging of crystal structures. The microscope's resolution is fundamentally limited by the de Broglie wavelength of the electrons. Calculate the de Broglie wavelength of the electrons after acceleration. Compare this to the wavelength of visible light (approximately 500  nm500\;\text{nm}) by finding the ratio λvisibleλelectron\frac{\lambda_{\text{visible}}}{\lambda_{\text{electron}}}. Given constants: Electron mass me=9.11×10−31  kgm_e = 9.11 \times 10^{-31}\;\text{kg}, elementary charge e=1.60×10−19  Ce = 1.60 \times 10^{-19}\;\text{C}, Planck's constant h=6.63×10−34  J⋅sh = 6.63 \times 10^{-34}\;\text{J·s}.

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