For x rays with wavelength 0.0300 nm, the m = 1 inten- sity maximum for a crystal occurs when the angle u in Fig. is 35.8°. At what angle u does the m = 1 maximum occur when a beam of 4.50 keV electrons is used instead? Assume that the electrons also scat- ter from the atoms in the surface plane of this same crystal. (2 The electronsare accelerated by4 The detector canbe moved to detectA heated filamentemits electrons.scattered electronselectrodes anddirected at a crystal.at any angle u.buVoltagesourceElectronbeam(in vacuum)3 Electrons strikea nickel crystal.VbaV - VaVba 7 0, so electrons speed up in moving from a to b.

λ=0.03nm=0.03×10-9mθ=35.8m=1Energy E=4.5keVD=mλsinθ=1×0.03×10-9msin35.8=5.12×10-4m

(2 The electrons are accelerated by 4 The detector can be moved to detect A heated filament emits electrons. scattered electrons electrodes and directed at a crystal. at any angle u. b u Voltage source Electron beam (in vacuum) 3 Electrons strike a nickel crystal. Vba V - Va Vba 7 0, so electrons speed up in moving from a to b.

(2 The electrons are accelerated by 4 The detector can be moved to detect A heated filament emits electrons. scattered electrons electrodes and directed at a crystal. at any angle u. b u Voltage source Electron beam (in vacuum) 3 Electrons strike a nickel crystal. Vba V - Va Vba 7 0, so electrons speed up in moving from a to b.