Chapter 12, Problem 12.85QP

(a)

Interpretation Introduction

Interpretation: In Buckminsterfullerene, ${\text{C}}_{60}$ molecules are given to form a cubic closest-packed array of spheres with a unit cell edge length of $1410\text{pm}$. The density of crystalline ${\text{C}}_{60}$ and the radius of the ${\text{C}}_{60}$ molecule is to be calculated.

Concept introduction: The density of crystalline ${\text{C}}_{60}$ is calculated by formula,

$d=\frac{Z\times M}{a^3\times {\text{N}}_{\text{A}}}$

The relationship between atomic radius and edge length of cubic is,

$a=2r$

To determine: The density of ${\text{C}}_{60}$ molecule.

(b)

Interpretation Introduction

To determine: The radius of the ${\text{C}}_{60}$ molecule.