Question

If the total number of atoms per unit cell in a hcp structure and a bcc structure get halved , then ratio of % voids in hcp and bcc structures is

1) 34/27

2) 21/22

3) 22/21

4) 37/34

Answer 1

answer : option (2) 21/22

explanation : we know, in hexagonal close packed structure (hcp) ; atoms occupy 74% and 28% empty space(voids).

and in body centered cubic structure(bcc) ; atoms occupy 68% and 32% empty space(voids)

now, if If the total number of atoms per unit cell in a hcp structure and a bcc structure get halved.

atoms occupy in hcp = 74/2 = 37%

and voids = (100 - 37) = 63%

atoms occupy in bcc = 68/2 = 34%

and voids = (100 - 34) = 66%

so, ratio of their voids = 63%/66% = 21/22

hence, option (2) is correct choice.

Answer 2

your correct option is 2