On a certain crystal, a first-order X-ray diffraction maximum is observed at an angle of 27.1° relative to its surface, using an X-ray source of unknown wavelength. Additionally, when illuminated with a different known wavelength of 0.137 nm, a second-order maximum is detected at 37.3°. Determine a. the spacing between the reflecting planes.  b. the unknown wavelength.

University Physics Volume 3
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Chapter4: Diffraction
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Problem 76P: On a certain crystal, a first-order X-ray diffraction maximum is observed at an angle of 27.1°...
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On a certain crystal, a first-order X-ray diffraction maximum is observed at an angle of 27.1° relative to its surface, using an X-ray source of unknown wavelength. Additionally, when illuminated with a different known wavelength of 0.137 nm, a second-order maximum is detected at 37.3°. Determine

a. the spacing between the reflecting planes. 

b. the unknown wavelength.

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