In which of the following close-packed structures, the radii r of their spheres respectively is correctly represented?
Answer & explanation
Correct answer: option 2
The correct answer is option 2. \(\text{hcp, ccp : }\frac{a}{2\sqrt{2}}, \frac{a}{2\sqrt{2}}\).
In Hexagonal close packing (hcp),
\(4r = \sqrt{2}a\)
or, \(r \frac{\sqrt{2}a}{4}\)
or, \(r = \frac{a}{2\sqrt{2}}\)
In Cubic close packing
\(4r = \sqrt{2}a\)
or, \(r \frac{\sqrt{2}a}{4}\)
or, \(r = \frac{a}{2\sqrt{2}}\)
Thus the answer is option 2. \(\text{hcp, ccp : }\frac{a}{2\sqrt{2}}, \frac{a}{2\sqrt{2}}\)