Discussion Forum

The correct statement (s) for cubic close packed (ccp) three dimensional structure is (are)

Answer:

Explanation:

(a)  Nearest neighbour in the topmost  layer of ccp structure is 9 thus, incorrect

(b) Packing efficiency is 74% thus, correct

(c) Tetrahedral voids=2

 Octahedral  voids= 1 per atom thus, correct.

 (d) Edge length,

                   $a=\frac{4}{\sqrt{2}}r=2\sqrt{2}r$

thus, correct explanation

Edge length=a, Radius=r

 $AC^{2}=AB^{2}+BC^{2}$

$(4r)^{2}=a^{2}+a^{2}=2a^{2}$

$4r=\sqrt{2}a\Rightarrow r=\frac{\sqrt{2}}{4}a=\frac{a}{2\sqrt{2}}$

$\therefore  a=2\sqrt{2}r$

In ccp structure, the number of sphere is 4, 

Hence , volume of 4 spheres=  $4(\frac{4}{3}\pi r^{3})$

Total volume of unit cell= $a^{3}=(2\sqrt{2}r)^{3}$

% of packing efficiency= $\frac{volume. of 4 spheres}{ volume .of unit cell}$

=  $\frac{4(\frac{4}{3}\pi r^{3})}{(2(\sqrt{2}r))^{3}}\times100=74.05$%= 74%