Question

Aluminium (atomic mass = 27) crystallises in a cubic system with edge length of 4A. 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

The correct option is C 4

Given, edge length of cubic system
$=4A^o=.4\times {10}^{-8}cm$

density $=2.7gc{m}^{-3}$ and mass
= 27 g/mol

So, the number of aluminium atoms present per unit cell
$\left(Z\right)=\frac{d\times a^3\times N_A}{m}$
$=\frac{2.7\times (4\times {10}^{-8}{)}^3\times 6.022\times {10}^{23}}{27}$

$3.85\simeq 4$