What is the atomic spacing D of this crystal?

[spaghed87]

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:

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.

 

[TeethWhitener]

(Note to others: OP is using $\theta$ defined relative to the normal of the plane, rather than parallel, hence the appearance of the cosine rather than the more usual sine in the Bragg condition.)

OP, you have correctly determined that the distance between the crystal planes is 0.16 nm. However, the problem is looking for the distance between atoms, so you’ll need to use the crystal geometry to solve for D.