In powder XRD of copper (FCC) with Cu Kα radiation (wavelength 0.15406 nm), the lowest-angle peak appeared at 2θ = 43.30°. Which value is closest to the lattice parameter of copper?

Answer: C. About 0.362 nm

θ = 21.65° and sinθ ≈ 0.3689, so Bragg's law gives d = λ/(2 sinθ) ≈ 0.2088 nm. In FCC the lowest-angle peak is (111), so a = d × √(1² + 1² + 1²) = 0.2088 × √3 ≈ 0.362 nm, matching the lattice parameter of copper (about 0.3615 nm). About 0.209 nm is the interplanar spacing d itself, without converting to the lattice parameter. About 0.295 nm treats the first peak as (110) and multiplies by √2, the mistake of applying the BCC extinction rules. Correct indexing of the peaks is a prerequisite for determining the lattice parameter.