Question

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 ?

Answer 1

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

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

Explanation:

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 `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"`