Question

Calculate the number of unit cells in $8.1g$ of aluminium if it crystallizes in a face-centred cubic (f.c.c.) structure? (Atomic mass of $Al=27gmo{l}^{-1})$

Answer 1

Given that,

Mass of aluminium, $w=8.1g$

Number of atoms of $Al,N_{Al}=\frac{Mass}{Molarmass}\times N_A=\frac{w}{M}\times N_A=\frac{8.1}{27}\times N_A$

There are $4$ atoms present per unit cell as it crystallizes in a face-centred cubic (f.c.c.) structure.

Therefore, number of unit cells $=\frac{8.1\times 6.023\times {10}^{23}}{27\times 4}=4.52\times {10}^{22}\text{unit cells}$