Question

Aluminium crystallizes in a cubic close packed structure. Its metallic radius is $125$ pm. The edge length (in pm) of the unit cell and number of unit cells per cc of aluminium, respectively, are :

• A. $354,$ $2.25\times {10}^{22}$
• B. $648,$ $3.3\times {10}^{23}$
• C. $298,$ $25\times {10}^{22}$
• D. $436,$ $6.3\times {10}^{22}$

Answer 1

The correct option is A $354,$ $2.25\times {10}^{22}$

Given that the metallic radius $=r=125$ pm

In CCP, we have$\sqrt{2}a=4r$

$a=354$ pm

Volume of one unit cell is $(354\times {10}^{-10}{)}^3$.

Number of unit cells $=\frac{\text{Total volume}}{\text{Volume of unit cell}}$ $\frac{1c{m}^3}{(354\times {10}^{-10}{)}^3{cm}^3}=2.25\times {10}^{22}$