Question

In a close-packed body-centred cubic lattice of potassium, the correct relation between the atomic radius $(r)$ of potassium and the edge-length $(a)$ of the cube is

• A. $r=\frac{a}{\sqrt{2}}$
• B. $r=\frac{a}{\sqrt{3}}$
• C. $r=\frac{\sqrt{3}}{2} a$
• D. $r=\frac{\sqrt{3}}{4} a$

Answer 1

Answer: (D)

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

Answer 2

$\because$ For be packing, $\sqrt{3} a=4 r$ $\therefore r=\frac{\sqrt{3}}{4} \cdot a$ where $a=$ edge length $r=$ radius of lattice sphere