   # Barium has a body-centered cubic structure. If the atomic radius of barium is 222 pm, calculate the density of solid barium. ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243

#### Solutions

Chapter
Section ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 9, Problem 58E
Textbook Problem
95 views

## Barium has a body-centered cubic structure. If the atomic radius of barium is 222 pm, calculate the density of solid barium.

Interpretation Introduction

Interpretation:

Density of solid Barium made of body-centered cubic structure has to be determined.

Concept introduction:

In packing of atoms in a crystal structure, the atoms are imagined as spheres. The two major types of close packing of the spheres in the crystal are – hexagonal close packing and cubic close packing.

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

Each atom in the corner is shared by eight unit cells and a single atom in the center of the cube remains unshared. Thus the number of atoms per unit cell in BCC unit cell is,

8×18atomsincorners+1atomatthecenter=1+1=2atoms       The edge length of one unit cell is given bya=4R3where  a=edge length of unit cellR=atomic radius

### Explanation of Solution

Explanation

Calculate the volume of unit cell of solid barium.

givendata:R=222pm=222×10-12ma=4R3=4×222×10-12m1.732=512.7pm

volume of unit cell=a3=(512.7×10-12)3m3=1.35×10-22cm3=13.5×10-23cm3

Atomic radius of the Barium is given. Atomic radius and the edge length of a unit cell is related by the equation a=4R3 where ‘a’ corresponds to edge length and ‘R’ corresponds to atomic radius. Upon substituting ‘R’ value ‘a’ value is obtained. Volume of a BCC unit cell is obtained from the cubic value of edge length.

Calculate the mass of unit cell of Barium.

Average mass of one Ba atom=atomicmassofBaAvogadronumber=137.33g6.022×1023=22

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