Welcome to ChemZipper !!!: If the total number of atoms per unit cell in an hcp structure and a bcc structure gets halved, then ratio of percentage voids in hcp and bcc structures is

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

In HCP ; Packing efficiency:
Atoms occupy:74%
Empty space(voids): 28% 
In BCC; Packing efficiency:
Atoms occupy: 68% 
Empty space(voids): 32% 
According to the given condition if the total number of atoms per unit cell in a hcp structure and a bcc structure get halved. Then packing efficiency in HCP and BCC respectively given as:

In HCP ; Packing efficiency:
Atoms occupy: 74/2 = 37%
Empty space(voids): (100 - 37) = 63%
In BCC; Packing efficiency:
Atoms occupy: 68/2 = 34%
Empty space(voids): (100 - 34) = 66%

Then new ratio of their voids = 63%/66% = 21/22

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