Question

Calcium crystallizes in a cubic unit cell with density 3.2 g/cc. Edge length of the unit cell is 437 pm.

The type of unit cell is :

• A. simple cubic
• B. body-centred cubic
• C. face-centred cubic
• D. edge-centred

Answer 1

Answer: (C)

face-centred cubic

The density of the crystal can be found out by applying the formula as follows:
$d=\frac{M\times Z}{N_0\times a^3}$

where $d=$ density of the crystal,
$M=$ atomic or molecular weight of the species,
$Z=$ number of atoms in the unit cell,
$N_0$ = Avogadro number,
$a=$ edge length.

We have to find out the value of $z$ in order to determine the type of unit cell.

From the above equation, we have $Z=d\times N_0\times \frac{a^3}{M}$

Now substituting the different values in the above equation,
$z=\frac{3.22\times 6.022\times {10}^{23}\times (437\times {10}^{-10}{)}^3}{40}$

$z=4.04\approx 4.0$

Since $z=4$, the type of unit cell is face centred cubic (fcc).