The (002) plane of an elemental FCC crystal diffracts X-rays ( $\lambda=0.154\,\mathrm{nm}$ ) at Bragg angle $90^{\circ}$. the density of the crystal is $4 \times 10^{4}\,\mathrm{kg}\,\mathrm{m}^{-3}$. The atomic weight of the elemental solid is
(a)22
(b)44
(c)88
(d)66
Answer
Answer: A ✓ checked by 4AB · confidence high
Explanation
θ = 90°: λ = 2d₀₀₂ ⇒ d₀₀₂ = 0.077 nm ⇒ a = 0.154 nm. M = ρN_Aa³/4 = 4×10⁴ × 6.022×10²³ × (1.54×10⁻¹⁰)³/4 = 0.022 kg mol⁻¹ = 22 g mol⁻¹.