The Crystal Authenticator · AI Generator #GEN-51B593A9
Physics · modern-physics
Problem
A gemologist uses X-ray diffraction to authenticate crystals. She has developed a portable device that uses characteristic X-rays from a copper target (wavelength λ=1.54×10−10m) to identify unknown crystal samples.
When examining a suspected quartz crystal, she observes a strong diffraction peak at an angle θ=13.2° from a particular set of crystal planes. The spacing between these planes in authentic quartz is known to be d=4.26×10−10m.
To verify her equipment is working correctly, she also tests the X-ray beam using a thin graphite sample as a Compton scattering target. She measures scattered X-rays at an angle of 90° relative to the incident beam.
(a) Is the crystal sample authentic quartz? Support your answer with a calculation.
(b) What is the wavelength of the X-rays scattered by the graphite at 90°? (Use mec2=0.511MeV and hc=1.24×10−6eV⋅m)