Q1(h). Lattice spacing from Bragg’s law

Answer in brief

θ = 30°, so d = λ/(2 sin θ) = 1.539 Å (153.9 pm).

Key points

• The angle recorded is 2θ, between the undeviated and the diffracted beam; Bragg angle θ = 30°, sin θ = 0.500.
• Bragg’s law: the rays reinforce when the path difference 2d sin θ equals nλ.
• d = nλ/(2 sin θ) = 1 × 1.539/(2 × 0.500) = 1.539 Å = 153.9 pm.
• Here d = λ because sin 30° = ½; for a cubic metal a = d(h² + k² + l²)^½ once the reflection is indexed.