When x-rays of wavelength 0.312 nm are directed at a crystalline sample, the smallest bragg angle for a certain family of reflecting planes is found to be 28.5°. within the sample, the atoms lie on a simple cubic lattice, a 2-dimensional view of which is shown to the right. assuming that the constructive interference observed is due to the pair of diagonal planes indicated by the two dashed lines, find the distance a between neighboring atoms?

Question

Physics

Carsen

25 January, 18:43

When x-rays of wavelength 0.312 nm are directed at a crystalline sample, the smallest bragg angle for a certain family of reflecting planes is found to be 28.5°. within the sample, the atoms lie on a simple cubic lattice, a 2-dimensional view of which is shown to the right. assuming that the constructive interference observed is due to the pair of diagonal planes indicated by the two dashed lines, find the distance a between neighboring atoms?

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Justice Hartman · Answer 1

The equation for bragg's law is nλ=2dsinθ. The smallest angle is when n=1 and we are told the angle is 28.5. d in our equation is the distance between atoms. So:

(1) (0.312*10^-9) = 2dsin (28.5)

Solving for d we get

d=3.26925*10^-10m