Discussion Forum



1)

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


A) $\frac{1}{2}a:\frac{\sqrt{3}}{4}a:\frac{1}{2\sqrt{2}}a$

B) $\frac{1}{2}a:\sqrt{3}a:\frac{1}{\sqrt{2}}a$

C) $\frac{1}{2}a:\frac{\sqrt{3}}{2}a:\frac{\sqrt{3}}{2}a$

D) $1a:\sqrt{3}a:\sqrt{2}a$

Answer:

Option A

Explanation:

Following generalization can be easily derived for various types of lattice arrangements in cubic cells between the edge length (c) of the cell and r the radius of the sphere

For simple cubic: a = 2r or r = a/2

For body centred cubic : a = $\frac{4}{\sqrt{3}}$ r or r = $\frac{\sqrt{3}}{4}$a

For face centred cubic : a = $2\sqrt{2}r$ or r = $\frac{1}{2\sqrt{2}}a$

Thus the ratio of radii of spheres for these will be

simpte : bcc : fcc = $\frac{1}{2}a:\frac{\sqrt{3}}{4}a:\frac{1}{2\sqrt{2}}a$

option (a) is correct answer.