Your x-ray lab has a monochromator consisting of a single crystal of nickel cut so that the plane lies in the cube face. At what angle (in degrees) should the cube face be tilted with respect to the incident beam in order to select radiation with a wavelength ? The lattice constant of nickel is .

(111) plane

wavelengt ambda= 3.091 A
lattice constant is alpha = 3.53 A

n*wavelength = 2d*sin theta.

I presume you want n = 1.

To determine the angle at which the cube face should be tilted with respect to the incident beam in order to select radiation with a specific wavelength, we need to consider the Bragg's law.

Bragg's law states that for constructive interference to occur in a crystal lattice, the path difference between two adjacent scattering planes must be equal to an integer multiple of the wavelength.

Mathematically, Bragg's law is given by:
2d sin(θ) = nλ
where:
- d is the spacing between the scattering planes in the crystal lattice (in this case, the lattice constant of nickel),
- θ is the angle between the incident beam and the scattering plane,
- n is the order of the diffraction peak (typically 1 for the primary peak),
- λ is the wavelength of the incident beam we want to select.

In this case, we want to select radiation with a specific wavelength λ, so we rearrange Bragg's law to solve for the angle θ:
θ = arcsin(nλ / (2d))

Given that the lattice constant d of nickel is provided, and we have the desired wavelength, you can substitute these values into the equation to calculate the angle θ.