Bragg diffraction / Solid state physics

[vorcil]

Homework Statement

Homework Equations

$$n\lambda = 2dsin(\theta)$$

The Attempt at a Solution

a)

solving for d I get
$$\frac{n*\lambda}{2*sin*(\theta)} = d$$

substituting in the first value 50.85 to solve for d, with n=1
I get d= 1.754*10^-10m

How do I solve the miller indices from the inter particle spacing?

I do not know a, the length of the side of a cubic cell of the crystal
can I just use 1 for that?

$$d= \frac{{n*a}{h^2+k^2+l^2}}$$

h k l being the indices, all of which are integers

 

[vorcil]

How do i determine the lattice constant a?

I know it's a cubic crystalline material
and I know the diffraction angles but how do i figure a out!

 

[vorcil]

Are there alternative methods to solving the miller indices?