Exam

JIPMER

Year

2010

Subject

Chemistry

Chapter

Solid State

JIPMER 2010 · Chemistry · Solid State

If a be the edge length of the unit cell and r be the radius of an...

If $a$ be the edge length of the unit cell and $r$ be the radius of an atom then for fcc arrangement, the correct relation is

Step-by-step solution

Given, the edge length of the unit cell $=a$ and, radius of the sphere $=r$ Consider $\triangle A B C$, $$\begin{aligned} A C^2 & =A B^2+A C^2 \\ & =a^2+a^2 \\ & =2 a^2 \\ \therefore \quad A C & =\sqrt{2} \cdot a \end{aligned}$$ But, from the figure, $A C=4 r \therefore \quad 4 r=\sqrt{2} \cdot a$