Your x-ray lab has a monochromator consisting of a single crystal of nickel cut so that the (001) 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 λ=3.091 A˚? The lattice constant of nickel is a=3.53 A˚.
Bragg's Law will get it for you.
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thanks
how about the calculation? not the result
To select radiation with a specific wavelength using a crystal monochromator, we need to use Bragg's law, which states that the condition for constructive interference in a crystal lattice is given by:
nλ = 2dsinθ
where n is the order of diffraction, λ is the wavelength of the incident beam, d is the spacing between the crystal lattice planes, and θ is the angle of incidence.
In this case, we want to select radiation with a wavelength of λ = 3.091 Å, and the lattice constant (spacing between the crystal lattice planes) of nickel is given as a = 3.53 Å.
Since the (001) plane of the crystal lies in the cube face, the spacing between the (001) planes can be calculated using the formula:
d = a / √(h^2 + k^2 + l^2)
where h, k, and l are the Miller indices of the plane of interest. In this case, h = 0, k = 0, and l = 1, because we're considering the (001) plane.
Substituting these values into the formula, we get:
d = a / √(0^2 + 0^2 + 1^2)
= a / √1
= a
So, the spacing between the (001) planes is equal to the lattice constant.
Now, we can rearrange Bragg's law to solve for the angle of incidence, θ:
θ = arcsin(nλ / 2d)
Substituting the given values, we have:
θ = arcsin(nλ / 2a)
Plugging in λ = 3.091 Å and a = 3.53 Å, we get:
θ = arcsin(n * 3.091 Å / 2 * 3.53 Å)
Note: The value of n is not provided in the question. The angle of incidence will depend on the order of diffraction, which is specified in the experiment or required application. If you have a specific value for n, substitute that value into the equation to calculate the angle of incidence.