In XRD with Cu Kα radiation (wavelength 0.15406 nm), which value is closest to the diffraction angle 2θ of the first-order peak from the Si (111) planes, with an interplanar spacing of 0.3135 nm?

Answer: B. About 28.4°

From Bragg's law 2d sinθ = nλ (n = 1), sinθ = 0.15406/(2 × 0.3135) ≈ 0.2457, so θ ≈ 14.2° and the diffraction angle is 2θ ≈ 28.4°. XRD instruments and data normally plot 2θ, the angle between the incident and diffracted X-rays, on the horizontal axis. About 14.2° is the mistake of answering θ itself, and about 58.9° drops the 2 in Bragg's equation and uses sinθ = λ/d. The peak of silicon powder near 28.4° is strong and sharp, so it is also widely used as a standard for calibrating diffraction angles.