The cubic unit cell of a metal (molar mass $=63.55 \mathrm{~g} \mathrm{~mol}^{-1}$ ) has an edge length of…
The cubic unit cell of a metal (molar mass $=63.55 \mathrm{~g} \mathrm{~mol}^{-1}$ ) has an edge length of $362 \mathrm{pm}$. Its density is $8.92 \mathrm{~g} \mathrm{~cm}^{-3}$. The type of unit cell is
primitive
face centred
body centred
end centred
Solution
Density, $d=\frac{M Z}{N_0 a^3}$
where, $Z=$ number of atoms in unit cell
$\begin{aligned}
\therefore \quad Z & =\frac{d N_0 a^3}{M} \\
& =\frac{8.92 \times 6.023 \times 10^{23} \times\left(362 \times 10^{-10}\right)^3}{63.55} \\
& =4.0
\end{aligned}$
Thus, metal has face centred unit cell.