Question

Aluminium (atomic mass = $27$) crystallizes in a cubic system with edge length of $4 \, \mathring{A}$. Its density is $2.7 \,g \,cm^{-3}$. 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 $=2.7\, g\, cm ^{-3}$ and mass

$=27\, g / mol$

So, the number of aluminium atoms present per unit cell

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

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

$=3.85 \simeq 4$