Question

Titanium metal has a density of $4.54gc{m}^3$ and a unit cell volume of $7\times {10}^{-23}c{m}^3$. In which cubic unit cell does titanium crystallise?
Given : $\text{Molecular mass of}Ti=48gmo{l}^{-1}$

• A. Hexagonal close packing
• B. Face centred cubic
• C. Simple Cubic
• D. Body centred cubic

Answer 1

The correct option is B Face centred cubic

Density of the unit cell,
$\rho =\frac{Z\times M}{N_A\times a^3}$
where,
$Z=\text{No. of atoms in a unit cell}M=\text{Molecular mass}{N}_A=\text{Avagadro number}$
$a^3=\text{Volume of the unit cell}$

$\rho =4.54g/c{m}^{3}M=48gmo{l}^{-1}$
$N_A=6.023\times {10}^{23}mo{l}^{-1}$
$Z=\frac{\rho \times N_A\times a^3}{M}$

$Z=\frac{4.54\times 6\times {10}^{23}\times 7\times {10}^{-23}}{48}=3.97\approx 4$

Thus, titanium has face-centred cubic structure