# Rubidium metal has a body-centered cubic structure (with one atom at each lattice point). The density of the metal is 1.532 g/cm 3 . From this information and the atomic mass, calculate the edge length of the unit cell. Now assume that rubidium atoms are spheres. Each corner sphere of the unit cell touches the body-centered sphere. Calculate the radius of a rubidium atom.

### General Chemistry - Standalone boo...

11th Edition
Steven D. Gammon + 7 others
Publisher: Cengage Learning
ISBN: 9781305580343

Chapter
Section

### General Chemistry - Standalone boo...

11th Edition
Steven D. Gammon + 7 others
Publisher: Cengage Learning
ISBN: 9781305580343
Chapter 11, Problem 11.114QP
Textbook Problem
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## Rubidium metal has a body-centered cubic structure (with one atom at each lattice point). The density of the metal is 1.532 g/cm3. From this information and the atomic mass, calculate the edge length of the unit cell. Now assume that rubidium atoms are spheres. Each corner sphere of the unit cell touches the body-centered sphere. Calculate the radius of a rubidium atom.

Interpretation Introduction

Interpretation:

• Edge length of unit cell of Rubidium metal has to be calculated.
• Radius of a Rubidium atom has to be calculated.

Concept introduction:

• Crystal structure: Crystal structure is arrangement of group of atoms or ions or molecule in the crystalline material.
• Unit cell: A simplest repeating unit in the crystal structure.  Every unit cell is described in terms of lattice point.  Example for unit cell: cubic, monoclinic, tetragonal, orthorhombic, rhombohedral, hexagonal and triclinic.
• Body centred cubic: Body cantered cubic cell is the type of crystal structure in metal.  This cubic structure cab be seen as a congregation of cubes with atoms at the edges and in the canter of all cube.

### Explanation of Solution

Given data

Density of the atom = 1.152 g/cm3

To determine: Edge length of the unit cell

2 Rb atoms ×1mol Rb6.022×1023Rb atoms×85.468 g Rb1mol Rb= 2.8385×10-22g

Cell volume = 2.8385×10-221.532 g/cm3= 1.8528×10-22cm3

In a cubic cell all edges are the same length, so the edge length is,

l = V31.8528×10-22cm33=5.7009×10-8cm

Because the corner shapes touches the body centred sphere, the length of the body diagonal should be four times the radius of Rubidium atom

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