Question

For an ideal hcp structure, where the atomic spheres touch each other, the ratio of \(\dfrac{c}{a}\) is:

• A. \(1.333\)
• B. \(1.633\)
• C. \(1.433\)
• D. \(1.743\)

Hint:

The ideal axial ratio for hcp crystal is \(\frac{c}{a}=1.633\).

Answer 1

The Correct Option is B

Concept:
For an ideal hexagonal close packed structure, the ideal axial ratio is: \[ \frac{c}{a}=\sqrt{\frac{8}{3}} \]

Step 1: Calculate the value. \[ \frac{c}{a}=\sqrt{\frac{8}{3}} \] \[ \frac{c}{a}=\sqrt{2.666} \] \[ \frac{c}{a}=1.633 \]

Step 2: Final answer.
Thus, for ideal hcp structure: \[ \frac{c}{a}=1.633 \] \[ \therefore \text{Correct Answer is (B)} \]