A compound forms hexagonal close-packed structure. What is the total number of voids in 0.5 mol of it? How many of these are tetrahedral voids?

Number of atoms in close packaging = 0.5 mol
1 has 6.022 ×10 23  particles
So that
Number of close−packed particles
= 0.5 × 6.022 × 1023 = 3.011 × 1023
Number of tetrahedral voids = 2 × number of atoms in close packaging
Plug the values we get
Number of tetrahedral voids = 2 × 3.011 × 1023
                                                  = 6.022 × 1023
 Number of octahedral voids = number of atoms in close packaging
So that
Number of octahedral voids = 3.011 × 1023
Total number of voids = Tetrahedral void + octahedral void
                                       = 6.022 × 1023 + 3.011 × 1023 
                                       = 9.03 × 1023

 

We clearly know that  the total no. of particles

( let n),  n = no. of moles  * avagadro number

                 = 0.5 * 6.022 * 10^23

                 = 3.011 * 10^23 particles 

 

Also we know that that octahedral voids are equal 

To the number of particles of the packed structure while the tetrahedral voids are generally the double of the number of particles of the packed structure. 

 

Hence 

Octahedral voids =  n = 3.011 * 10^23 voids (O) 

And 

Tetrahedral voids = 2n  = 2  * 3.011 * 10^23

                                     = 6.022 * 10^23 voids (T) 

 

Total no.  of voids = (O) + (T) 

                                = 6.022 * 10^23 + 3.011 * 10^23

                                = 9.033 * 10^ 23 voids 

A compound forms hcp structure. What is the total number of voids in 0.5 mole of it? How many of these are tetrahedral voids?