Question

Aluminium having atomic mass 27g mol-1 crystallizes in face centred cubic structure find the number of aluminium atom in l0 g of it also,find the number of unit cells in the given quantity ?​

Answer 1

Answer:

Calculate the number of unit cells in 8.1 g of aluminium if it crystallizes in a face-centred cubic (f.c.c.) structure. (atomic mass of Al=27g mol^(-1)) 27 g of aluminium has 6.022×1023 atoms of Al. 8.1 g of aluminium as 6.022×102327×8.1=1.807×1023 atoms of Al.

Answer 2

The number of unit cells in the given quantity is $=2.23$×$10^{22}$ unit cells

Explanation:

• Given Aluminum has an atomic mass of 27g mol-1

• Crystal is face-centered cubic structure

• number of aluminium atoms in l0 g mass

         so w =$l0 g$

• the number of unit cells in the given quantity is to be calculated

       $Number of atoms of Al=\frac{Mass}{Molar mass}$×$N_{A}$

        =$\frac{w}{M}$×    $N_{A}$

         =$\frac{10}{27}$×$N_{A}$ where $N_{A} =6.023$×$10^{23}$

• There are 4 atoms present in the unit cell it will crystallize in a face-centered  cubic crystal

• On solving the above values we get the number of unit cells as

             =$\frac{10}{27}$×$6.023$×$10^{23}$

             $=2.23$×$10^{22}$ unit cells

• The number of unit cells in the given quantity is $=2.23$×$10^{22}$ unit cells