Question

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

• A. $\frac{1}{2}a:\frac{\sqrt{3}}{2}a:\frac{\sqrt{2}}{2}a$
• B. $1a:\sqrt{3}a:\sqrt{2}a$
• C. $\frac{1}{2}a:\frac{\sqrt{3}}{4}a:\frac{1}{2\sqrt{2}}a$
• D. $\frac{1}{2}a:\sqrt{3}a:\frac{1}{\sqrt{2}}a$

Answer 1

The correct option is C $\frac{1}{2}a:\frac{\sqrt{3}}{4}a:\frac{1}{2\sqrt{2}}a$

For simple cube,

$a=2r\Rightarrow r=a/2$

For body centered cubic ,

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

For face centered cubic,

$a=2\sqrt{2}r\Rightarrow r=\frac{a}{2\sqrt{2}}$

So, the ratio of radii in simple cubic to body centered to face centered is

$\frac{a}{2}:\frac{\sqrt{3}a}{4}:\frac{a}{2\sqrt{2}}$

So, the correct answer is option C.