The Quantum Microscope Resolution Limit · AI Generator #GEN-F119DCCF
Physics · modern-physics
Problem
A new type of electron microscope uses a beam of electrons to image atomic structures. The electrons are accelerated through a potential difference of V=50.0kV before hitting the sample. Due to quantum effects, the resolution limit of this microscope is fundamentally determined by the de Broglie wavelength of the electrons.
(a) Calculate the de Broglie wavelength of the electrons in this microscope.
(b) The microscope can just barely resolve two adjacent atoms in a crystal lattice when they are separated by a distance equal to half the de Broglie wavelength. If the microscope is used to study a simple cubic crystal structure where atoms are arranged in a regular grid, what is the minimum lattice parameter (distance between nearest-neighbor atoms) that can be resolved?
(c) To improve the resolution by a factor of 2, by what factor must the accelerating voltage be increased?
Given: Electron rest mass me=9.11×10−31kg, Planck's constant h=6.63×10−34J⋅s, electron charge e=1.60×10−19C.