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In comparing the wavelengths of two monochromatic x-ray lines, it is noted that line A gives a first-order reflection maximum at a glancing angle of 24° to the smooth face of a crystal. Line B, known to have a wavelength of 96 pm, gives a third-order reflection maximum at an angle of 60° from the same face of the same crystal. (a) Calculate the interplanar spacing. (b) Find the wavelength of line A.

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We have 2d sin 24° = λA

and 2d sin 60° = 3 × 96 pm,

which give (a) d = 166.28 pm (b) λA = 135.26 pm.

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