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Relation Between r and a

The edge leng...

Question

The edge lengths of the unit cells in terms of the radius of sphere constituting fcc, bcc and simple cubic unit cells are respectively .......

(a) $2 \sqrt{2 r}, \frac{4 r}{\sqrt{3}}, 2 r$ (b) $\frac{4 r}{\sqrt{3}}, 2 \sqrt{2 r}, 2 r$

(c) $2 r, 2 \sqrt{2 r}, \frac{4 r}{\sqrt{3}}$ (d) $2 r, \frac{4 r}{\sqrt{3}}, 2 \sqrt{2 r}$

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Solution

Answer: (a) Edge length for different types of unit cells can be tabulated as

$\begin{matrix} T y p e s o f u n i t c e l l & E d g e l e n g t h f c c & 2 \sqrt{2 r} b c c & \frac{4}{\sqrt{3}} r s c c & 2 r \end{matrix}$

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