Question

If the separation between the $1^{st}$ the $5^{th}$ layer in an ABCABC type crystal is $n\sqrt{\frac{2}{27}}r$ (r = radius of atom), then n is

Answer 1

The separation between two consecutive layers is = $\frac{\sqrt{3}}{3}a=\frac{2\sqrt{6}}{3}r(a=2\sqrt{2}r)$
The separation between $1^{st}$ and $5^{th}$ layers $=\frac{2\sqrt{6}}{3}r\times 4=24\sqrt{\frac{2}{27}}r$