   Chapter 12.6, Problem 3.3ACP

Chapter
Section
Textbook Problem

The density of gray tin is 5.769 g/cm3. Determine the dimensions (in pm) of the cubic crystal lattice.

Interpretation Introduction

Interpretation:

The dimension of the cubic crystal lattice in gray tin has to be calculated.

Concept introduction:

To find formula for the dimension of the atom is given below,

Length of one side=V3

Explanation

Number of atoms per unit is given below,

It has 8 atoms in the corner, 6 atom in the face, 4 atoms in the body.

Number of atoms per unit= (8corneratoms×1/8+6faceatom×1/2+4bodyatoms×1)Number of atoms per unit=8

density =5.769g/cm3molarmassoftin=118.710 g/mol

Z = number of atoms per unit.

The Avogadro number NA=6.02×1023

Massoftheunitcell=8 × 118.7106.023×1023Massoftheunitcell=1

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