In hcp (ABAB...) and ccp (ABCABC...) structures made up of spheres of equal size, the volume occupied per sphere (including the empty spaces) is ( a= radius of sphere) :

Question

In hcp (ABAB...) and ccp (ABCABC...) structures made up of spheres of equal size, the volume occupied per sphere (including the empty spaces) is ( a= radius of sphere) : (A) 5.66 a 3 (B) 1.33 a 3 (C) 2.66 a 3 (D) 7.40 a 3

Tardigrade Admin · Accepted Answer

so, volume of unitcell in ccp=((4 a/√2))3 so volume per spheric/atom =(1/4) × (64 a3/2 √2) =0.566 a3.

Q. In hcp $(A B A B ...)$ and ccp $(A BC A BC ...)$ structures made up of spheres of equal size, the volume occupied per sphere (including the empty spaces) is ( $a =$ radius of sphere) :

$5.66 a^{3}$

$1.33 a^{3}$

$2.66 a^{3}$

$7.40 a^{3}$

so, volume of unitcell in $cc p = (\frac{4 a}{2})^{3}$
so volume per spheric/atom $= \frac{1}{4} \times \frac{64 a ^{3}}{2 2}$
$= 0.566 a^{3}$ .

Q. In hcp (ABAB...) and ccp (ABCABC...) structures made up of spheres of equal size, the volume occupied per sphere (including the empty spaces) is ( a= radius of sphere) :

5.66a3

1.33a3

2.66a3

7.40a3