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If 'a' stands for the edge length of the cubic systems : simple cubic, body centred cubic and face centred cubic, then the ratio of radii of the spheres in these systems will be respectively

$\begin {array} {1 1} (1)\;1a : \sqrt 3 a : \sqrt 2 a & \quad (2)\;\large\frac{1}{2}a : \large\frac{\sqrt 3}{4}a : \large\frac{1}{2\sqrt 2}a \\ (3)\;\large\frac{1}{2}a : \sqrt 3 a : \large\frac{1}{\sqrt 2 }a & \quad (4)\;\large\frac{1}{2}a : \large\frac{\sqrt 3}{2}a : \large\frac{\sqrt 2}{2}a \end {array}$

1 Answer

Solution :
For Simple cubic :
$\large\frac{r'}{r} =\frac{a}{2}$
Here a =edge length and
$\large\frac{r'}{r} =$ interatomic distance
For body centered
$r'+r = \large\frac{a}{2 \sqrt 2}$
Therefore , ratio of radii of the three will be
$\large\frac{a}{2} : \frac{a \sqrt 3}{4} :\frac{a}{2 \sqrt 2}$
answered May 23 by meena.p
 
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