Ncert Exercises & Solutions

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

1. $2 \sqrt{2 r}, \frac{4 r}{\sqrt{3}}, 2 r$

2. $\frac{4 r}{\sqrt{3}}, 2 \sqrt{2 r}, 2 r$

3. $2 r, 2 \sqrt{2 r}, \frac{4 r}{\sqrt{3}}$

4. $2 r, \frac{4 r}{\sqrt{3}}, 2 \sqrt{2 r}$

HINT: Check the relation between edge length and radius of an atom.

Explanation:

Edge length for different types of unit cells can be tabulated as

Types of the unit cell

Edge length

Fcc

Bcc

Simple cubic unit

$2 \sqrt{2} r$

$\frac{4}{\sqrt{3}} r$