Chemistry - Solid State Question with Solution | TestHub

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