A laboratory wants to look at detail on the scale of the atomic spacing
PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Condensed Matter, Materials & Soft Matter · Origins of quantum theory
Quantum Mechanics: From the Photon to the Hydrogen Atom, Ch Matter waves and wave-particle duality
Problem
A laboratory wants to look at detail on the scale of the atomic spacing, about 0.20 nm. Its light microscope uses green light of wavelength 550 nm; its electron instrument accelerates electrons through 10 kV, giving them a kinetic energy of 10 keV. Treat the electrons non-relativistically and use λ=1.226nm/K/eV. As a working rule, an instrument using waves of wavelength λ can just resolve detail of size λ/2.
((a)) Find the de Broglie wavelength of a 10 keV electron, in nm.
((b)) By what factor is it smaller than the wavelength of the green light?
((c)) State the finest detail each instrument can resolve, in nm, and say which of them can see the 0.20 nm atomic spacing.
((d)) The same electrons are sent through a thin crystal whose atomic rows are D=0.215 nm apart. Using Dsinθ=λ for the first-order peak, find the angle of that peak, in degrees, and say in one sentence what this implies about the length of the instrument's camera.