In X - Ray diffraction analysis the angle of the reflected beam for 1st order diffraction is $sf(21.9^@)$ . If the incident X - ray has a wavelength of $1.57color(white)(x)stackrel(@)"A"$ what is the separation of the crystal planes ?

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Answer 1 · 2015-12-12T15:33:11

$2.10color(white)(x)stackrel(@)"A"$

or $0.210color(white)(x)"nm"$

This question is based on X - ray diffraction.

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The incident X - ray beams are reflected off the crystal layers as shown in the graphic.

After reflection the beams interfere with each other to produce a pattern which can be detected with a photographic plate.

If the X - rays are in phase constructive interference occurs:

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This produces a pattern on the plate enabling $theta$ to be measured.

The condition for constructive interference to occur is that the path difference of the two beams must be a whole number of wavelengths.

From the graphic you can see that this path difference is $dsintheta$ going in + $dsintheta$ coming out.

Since this must be equal to a whole number of wavelengths $lambda$ we can write:

$nlambda=2dsintheta$

Where $n$ is an integer.

In this case $n=1$ so we can write:

$d=(lambda)/(2sintheta)$

$:.d=(1.57)/(2xx0.373)=2.10color(white)(x)stackrel(@)"A"$

The $stackrel(@)("A")"ngstrom"$ unit is not strictly SI. This is equal to $0.210color(white)(x)"nm"$

In X - Ray diffraction analysis the angle of the reflected beam for 1st order diffraction is sf(21.9^@)sf(21.9^@). If the incident X - ray has a wavelength of 1.57color(white)(x)stackrel(@)"A"1.57color(white)(x)stackrel(@)"A"what is the separation of the crystal planes ?