Question

Consider a metal with an FCC crystal structure. The interplanar spacing is known to be (2.0000x10^-1) nm. If the first-order angle of diffraction (2*theta) is found to be (4.50x10^1) ° for the (311) set of planes in this metal, what wavelength of monochromatic x-radiation (in nm) must have been used for the diffraction? Use scientific notation with 3 significant figures (X.YZ x 10^n). Note that Avenue automatically enters x10, so you only need to enter X.YZ and n.

Answer 1

Given: Interplanar spacing, d₃₁₁ = 2 x 10^-1 nm

            Diffraction Angle, 2θ_c = (4.5 x 10¹)^o = 45.0^o

To Find: Wavelength of Monochromatic X-Ray, λ = ?

Solution: For the above question, we are going to use the Bragg’s law equation:

                              nλ = 2d_hklsin(θ_c)

               Substituting the above values, we get,

                      For n = 1,

                                λ = 2d₃₁₁sin(2θ_c/2)

                                λ = 2 * 2 * 10^-1 * sin (45^o/2)

                                   = 1.53 * 10^-1 nm