Electron Microscope Resolution Limit · AI Generator #GEN-C287E0A9

Physics · modern-physics

Problem

A transmission electron microscope (TEM) accelerates electrons from rest through a potential difference of V=200  kVV = 200\;\text{kV} before they interact with a specimen. The resolution limit of the microscope is fundamentally determined by the de Broglie wavelength of the electrons - objects smaller than this wavelength cannot be clearly resolved. (a) Calculate the de Broglie wavelength of the electrons after acceleration. (b) What is the smallest feature size that can theoretically be resolved by this microscope? (c) How many times better is this resolution compared to visible light microscopy, which is limited by the wavelength of green light (λgreen=550  nm\lambda_{\text{green}} = 550\;\text{nm})? Given: electron rest 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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