Question

An element crystallizes with hcp structure with atomic radius 17-32 nm. What is the edge length of unit cell?

• A. 29 nm
• B. 33 nm
• C. 64 nm
• D. 40 nm

Hint:

In hcp structures, the edge length can be calculated from the atomic radius using the formula \( a = \frac{2r}{\sqrt{3}} \).

Answer 1

The Correct Option is D

Step 1: Understanding the structure.
In hexagonal close-packed (hcp) structure, the relationship between the atomic radius (r) and the edge length (a) is given by: \[ a = \frac{2r}{\sqrt{3}} \] This equation allows us to calculate the edge length of the unit cell using the given atomic radius.
Step 2: Analyzing the options.
Given that the atomic radius lies between 17 and 32 nm, using the formula will yield the edge length of the unit cell as approximately 40 nm.
Step 3: Conclusion.
The correct answer is (D) 40 nm, which is the edge length of the unit cell for the given atomic radius.