When X-rays of wavelength 0.212 nm are directed at a crystalline sample, the sma

Question

When X-rays of wavelength 0.212 nm are directed at a crystalline sample, the smallest Bragg angle for a certain family of reflecting planes is found to be 12.5°. 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.

When X-rays of wavelength 0.212 nm are directed at a crystalline sample, the smallest Bragg angle for a certain family of reflecting planes is found to be 12.5. 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. Number nm

Explanation / Answer

let,

wavelength of the x-ray,lambda=0.212*10^-9 m

theta,=12.5 degrees

use Bragg equation,

2*d*sin(theta)=m*lambda

2*d*sin(12.5)=1*0.212*10^-9

===> d=48.97*10^-9 m

and

distance between neibouring atoms is a=d/sqrt(2)

a=3.463*!0^-8 m

spacing between the atoms, a=48.97 nm

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