X-ray diffraction analysis of crystalline (buckminsterfullerene) shows that the crystal structure at — Solid State Chemistry Question
Question
X-ray diffraction analysis of crystalline $\text{C}_{60}$ (buckminsterfullerene) shows that the crystal structure at 300 K can be regarded as FCC with a one-molecule basis and unit cell edge length of $\sqrt{2} \text{ nm}$; the molecules are orientationally disordered due to rotation. The centre-to-centre distance (in nm) between nearest neighbour $\text{C}_{60}$ molecules in the solid at 300 K is
💡 Solution & Explanation
In a Face-Centred Cubic (FCC) lattice, the nearest neighbours are situated along the face diagonal. The distance between them is $\frac{a}{\sqrt{2}}$. Given $a = \sqrt{2} \text{ nm}$, the distance is $\frac{\sqrt{2}}{\sqrt{2}} = 1 \text{ nm}$. Therefore, correct answer is 1.