X-ray Diffraction Homework: Calculate d & a

[luitzen]

Homework Statement

X-ray diffraction is made with a copper tube as x-ray source. The tube generates molybdenum x-rays with a wave length of 0.709 A (A=Angstrom). In the interval 40-160 degrees 2theta reflections are found under the following angles:

40.450 degrees
58.408
73.398
86.995
100.873
115.809
133.202
154.764

Make use of 1/d^2=(h^2+k^2+l^2)/a^2 (cubic structures)

1) Calculate d
2) Calculate the cell constant a
3) There's a state of this material in a primitive cubic structure. Will this give more or less reflections in the same (40-160 degrees) interval?

Homework Equations

Bragg's Law: lambda=2*d*sin(theta)

The Attempt at a Solution

1) Rewrite Bragg's Law:
d=lambda/(2*sin(theta))
Fill it in the equation for cubic structures:
lambda and theta (above angles/2) are known, so d can be calculated
2) I'd say assume that the first angle is for h+k+l is 1 and calculate the answer. The answer sheet says that for h+k+l=even reflections are indexed (BCC) structure. However it is never stated what kind of cubic structure should be assumed and I don't know which values of h+k+l should be assumed.

In the textbook it is written that h^2+k^2+l^2 is always even and I perfectly understand that, but I don't get why h+k+l should be even for BCC structures.

 

[LightHero]

Could someone explain this to me?3)It would give less reflections, because a primitive cubic structure has less lattice points.