Question

Rhenium has an HCP crystal structure with atomic radius of 0.137 nm and c/a ratio as 1.615. Compute the volume of the unit cell for Rhenium.

(a)  0.0863 nm³ 

(b)  0.043 nm³ 

 (c)  0.863 nm³ 

 (d)  0.317 nm³ 

Answer 1

Correct option (a) 0.0863 nm³ 

Explanation:

The volume of unit cell for HCPV_C = c x basearea

The base area for HCP structure is 6R²√3

Given that, c = 1.615 a

 And = 2 R

 ∴ c  = 3.23 R

 Again, given that R = 0.137 nm

∴.V_C = 3.23 × 0.137 nm × 6 × (0.137 nm)² × √3

= 0.0863 nm³