Chapter 7, Problem 88A

Interpretation Introduction

Interpretation: The atomic radius of silver needs to be determined from the length of the edge of the unit cell.

Concept Introduction:

For a face-centered cubic arrangement, the relation between edge length and radius of the atom is as follows:

  $\sqrt{2a}=4r$

Here, a is the edge length and r is the radius of the atom.

Answer to Problem 88A

  $0.0226\text{ nm}$

Explanation of Solution

According to the question, silver crystallizes in a face-centered cubic arrangement. Here, there is a silver atom at the edge of each corner of the unit cell. The edge length, a is given 0.4086 nm thus, the radius of silver can be calculated as follows:

  $\sqrt{2a}=4r$

Substitute the values,

  $\begin{array}{c}\sqrt{2\left(0.4086\right)}=4r\\ 0.904=4r\\ r=\frac{0.904}{4}\\ =0.0226\text{ nm}\end{array}$

Conclusion

Thus, the radius of a silver atom is $0.0226\text{ nm}$ .