Falsite (not real crystal) is a unknown metallic isotope in crystalform. Atoms a

Question

Falsite (not real crystal) is a unknown metallic isotope in crystalform. Atoms are in cubical array. A crystal of Falsiteis studied by X-ray diffraction. When x-rays of wavelength0.2 nm strike it, the smallest non-zero angle at which peaks arefound occur when the detector is at 32 degrees. a) predict all other positions (up to 180 deg) where thedetector will find peaks. b) what is the lattice spacing of Falsite? c) if the density is 6 gm / cm^3, what is the mass of afalsite atom
*i have been trying to use n*(lambda) = 2*d*sin(theta), theta= 32, but have not been successful. a) predict all other positions (up to 180 deg) where thedetector will find peaks. b) what is the lattice spacing of Falsite? c) if the density is 6 gm / cm^3, what is the mass of afalsite atom
*i have been trying to use n*(lambda) = 2*d*sin(theta), theta= 32, but have not been successful.

Explanation / Answer

If the detector is at 32 deg then the angle of incidence is 16deg (32 deg is measured from the incident beam) in the formula is the angle between the incident beamand the face of the crystal = 2 d sin 16 d = 2 * 10E-10 / (2 * sin 16) = 3.63 * 10E-10 m = 3.63 * 10E-8cm Then 1 cm contains 1 / 3.63 * 10E-8 = 2.76 * 10E7 atoms So 1 cm3 contains 2.09 * 10E22 atoms and m = 6 / 2.09 * 10E22 = 2.87 * 10E-22 gm  (around 170 proton masses)

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