What is the atomic spacing D of this crystal?

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Homework Statement


X rays with wavelength 0.10 nm are incident on a crystal with a hexagonal crystal structure. The x-ray diffraction spectrum is shown in the figure.

Figure:
knight_Figure_24_40.jpg




What is the atomic spacing D of this crystal? (in nanometers)



Homework Equations



The Bragg condition:
2*D*cos(theta)=m*lamda where, m=1,2,3...


The Attempt at a Solution



(m+1)/(m) ==> cos(50.1)/cos(71.3) = (2/1)

(m+1)/(m)==> cos(15.8)/cos(71.3) = (3/1)

D=(2*lamda)/(2*cos(theta_2)==> (lamda)/cos(theta_2)==> (0.10nm)/cos(50.1)=0.16nm

I just followed a similair example in the book. Maybe I'm getting it wrong because I'm not factoring anything in about the hexagonal shape in my math? *Note: this is a challange problem.
 

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