Question

A molecule $A_{2}B$ (molar mass = 166.4) occupies a triclinic lattice with a = $5\stackrel{\circ }{A}$, b = $8\stackrel{\circ }{A}$, and c = $4\stackrel{\circ }{A}$. If the density of $A_{2}B$ is 5.2 $gc{m}^{-3}$, the number of molecules present in one unit cell is:
(Take $N_A=6\times {10}^{23}$)

• A. 2
• B. 3
• C. 4
• D. 5

Answer 1

The correct option is B 3

Given
density, d = $5.2gc{m}^{-3}$
We know, $\text{density}=\frac{\text{mass}}{\text{volume}}$
Here volume of the unit cell
$=5\times {10}^{-8}\times 8\times {10}^{-8}\times 4\times {10}^{-8}c{m}^{-3}$
Mass of one $A_{2}B$ molecule = $\frac{166.4}{6.022\times {10}^{23}}g$
Let, number of molecule present in one unit cell = $Z$

$\therefore 5.2=\frac{Z\times 166.4}{5\times 8\times 4\times {10}^{-24}\times 6\times {10}^{23}}$
$\Rightarrow Z=3$