Chapter 9, Problem 60QRT

Interpretation Introduction

Interpretation:

The unit cell edge length of gold having fcc arrangement under given condition has to be determined.

Concept Introduction:

Relationship of radius with edge length:

A fcc unit cell can be represented as given below.

Figure 1

In fcc, the corner spheres are in touch with the face centered sphere as shown in the above figure.  Hence, the face diagonal $AC=4R$.

Consider right angled triangle ACD.

  $\begin{array}{c}{\left(AC\right)}^2={\left(AD\right)}^2+{\left(DC\right)}^2\\ \\ =a^2+a^2=2a^2\\ \\ AC=\sqrt{2}a=4R\\ \\ R=\frac{\sqrt{2}}{4}a\left(or\right)a=\frac{4R}{\sqrt{2}}\end{array}$