   # Nickel has a face-centered cubic unit cell. The density of nickel is 6.84 g/cm 3 . Calculate a value for the atomic radius of nickel. ### 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 52E
Textbook Problem
53 views

## Nickel has a face-centered cubic unit cell. The density of nickel is 6.84 g/cm3. Calculate a value for the atomic radius of nickel.

Interpretation Introduction

Interpretation:

The density of nickel having face-centered cubic unit cell is given and its atomic radius has to be determined.

Concept introduction:

In packing of atoms in a crystal structure, the atoms are imagined as spheres and closely packed in a regular pattern. The two major types of close packing of the spheres in the crystal are – hexagonal close packing and cubic close packing. Cubic close packing structure has face-centered cubic (FCC) unit cell.

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,

8×18atomsincorners+6×12atomsinfaces=1+3=4atoms       The edge length of one unit cell is given bya=2R2where  a=edge length of unit cellR=radiusofatom

### Explanation of Solution

Explanation

Calculate the mass of a unit cell.

Average mass of one Ni atom=atomicmassofNiAvogadronumber=58.69g6.022×1023=9.746×10-23g

Eachunitcellhas4Niatoms.Therefore,massofaunitcell=4×averagemassofoneCaatom=4×9.746×10-23g=390×1024g

Each unit cell contains 4 Ni atoms. Therefore four times the average mass of one Ni atom gives mass of a unit cell.

Calculate the volume and edge length of the unit cell.

givendata:density=6.84g/cm3calculateddatafrompreviousstep:mass=390×10-24gdensity=massvolumevolumeofaunitcell,a3=massdensitya3=390×10-24g6.84g/cm3=57.02×10-24cm3a=(57

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