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 ?

1 Answer
Dec 12, 2015

Answer:

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

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

Explanation:

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"#