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 ?
This question is based on X - ray diffraction.
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:
This produces a pattern on the plate enabling
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
Since this must be equal to a whole number of wavelengths
In this case