Question

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

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

Answer 1

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

For Simple cubic :

$\frac{r^{\prime }}{r}=\frac{a}{2}$

Here a =edge length and

$\frac{r^{\prime }}{r}=$ interatomic distance

For body-centered

$r^{\prime }+r=\frac{a}{2\sqrt{2}}$

Therefore, the ratio of radii of the three will be-

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

Hence, the correct option is $C$