Question

Aluminium (atomic mass = $27$) crystallizes in a cubic system with edge length of $4\mathring{A}$. Its density is $2.7gc{m}^{-3}$. The number of aluminium atoms present per unit cell is

• A. 5
• B. 6
• C. 4
• D. 2
• E. 3

Answer 1

Answer: (C)

Given, edge length of cubic system

$=4\mathring{A}=4\times 10^{-8}cm$

density $=2.7gc{m}^{-3}$ and mass

$=27g/mol$

So, the number of aluminium atoms present per unit cell

$(Z)=\frac{d\times a^3\times N_A}{m}$

$=\frac{2.7\times {\left(4\times 10^{-8}\right)}^3\times 6.022\times 10^{23}}{27}$

$=3.85\simeq 4$