Chapter 10, Problem 10.85SP

Interpretation Introduction

Interpretation:

The radius (in pm) of Lead atom and density (in $\text{g}{\text{cm}}^{\text{-3}}$) of Lead atom has to be given.

Concept Introduction:

Face-centered cubic:

In face-centered cubic unit cell, each of the six corners is occupied by every single atom.  Each face of the cube is occupied by one atom.

Each atom in the corner is shared by eight unit cells and each atom in the face is shared by two unit cells.  Thus the number of atoms per unit cell in FCC unit cell is,

$\text{8}\text{×}\frac{\text{1}}{\text{8}}\text{atoms}\text{in}\text{corners}\text{+}\text{6}\text{×}\frac{\text{1}}{\text{2}}\text{atoms}\text{in}\text{faces}\text{=}\text{1}\text{+}\text{3}\text{=}\text{4}\text{atoms}$

Density:

Density can be defined as property that links mass of an object to its volume.  It is derived quantity and its unit is $\text{g}{\text{ml}}^{\text{-1}}$ for liquids and $\text{g}{\text{cm}}^{\text{-3}}$ for solid.  The density of material can be calculated with the help of formula,

$\text{Density = }\frac{\text{Mass}\left(\text{g}\right)}{\text{Volume}\left(\text{ml}\text{or}{\text{cm}}^{\text{3}}\right)}$