X-Ray Diffraction Homework: Find Crystal Spacing

[JQ10]

Homework Statement

An X Ray beam (wavelength 10^10m) is incident upon a sample of a powdered crystalline material. At a distance of 5m from the sample a flat detecting film has been placed. A pattern of 2 circles have been recorded on this film (radius 2cm and 3.5cm).

What crystal spacing does this pattern correspond to?

Homework Equations

I'm not sure but:

mλ = 2dsinθ

(The reason I am unsure as that is for solid crystals not powder)

The Attempt at a Solution

So far I ahve calculated the angles the circles are at to the beam:

tan θ = 2/5 so θ = 22 degrees

tan θ = 3.5/5 so θ = 35 degrees

Next I tried putting them both into the above equation trying to calculate d but that makes little sense to me.

Anyone able to help?

 

[AvroArrow]

The equation you have uses the Bragg Diffraction principle which is valid for single crystal only. Since this is a powdered sample, the diffraction will be from many crystals in a random orientation. Hence, you cannot use the Bragg equation to find the crystal spacing.