Electrons leave a gun after being accelerated through a potential difference of V and…
PHYSICS · Multi-part · Fermi University Physics · Oscillations, Waves & Acoustics · Quantum Mechanics · Origins of quantum theory
Quantum Mechanics: From the Photon to the Hydrogen Atom, Ch Matter waves and wave-particle duality
Problem
Electrons leave a gun after being accelerated through a potential difference of 64 V and strike, at right angles, the flat face of a crystal whose surface atomic rows are D=0.250 nm apart. A detector swung round in the plane of the beam records the scattered electrons. The rows act as a reflection grating, so a peak appears at the angle θ given by Dsinθ=nλ with n=1,2,…; take the electrons to be non-relativistic and ignore any change of wavelength inside the crystal.
((a)) Find the de Broglie wavelength of the electrons.
((b)) Predict the angle of the first-order (n=1) peak.
((c)) The accelerating voltage is raised to 100 V. Predict the new first-order peak angle.