Question

Fullerene (C₆₀) crystallizes in an FCC unit cell (edge length = 14.14 Å) with one C₆₀ centered at each lattice point. The smallest distance (in Å) between the centers of two C₆₀ molecules is ..........
(Round off to two decimal places)

Hint:

In an FCC unit cell, the smallest distance between centers of molecules is the face diagonal, calculated as \( \sqrt{2}a \).

Answer 1

Correct Answer: 9.9

Step 1: Understanding the FCC structure.
In a face-centered cubic (FCC) unit cell, the molecules are located at the corners and face centers of the unit cell. The distance between two centers of C₆₀ molecules corresponds to the edge length of the unit cell. The distance is the face diagonal for an FCC structure.

Step 2: Calculation.
The face diagonal \( d \) of an FCC unit cell is given by \( d = \sqrt{2}a \), where \( a \) is the edge length. Substituting \( a = 14.14 \, \text{Å} \), we get: \[ d = \sqrt{2} \times 14.14 = 20 \, \text{Å} \] Thus, the smallest distance between two C₆₀ molecules is \( \boxed{20.00} \, \text{Å} \).