Chemistry - Solid State Question with Solution | TestHub

The density of a cubic unit cell is given by the formula:

$d=\frac{Z\times M}{a^3\times N_A}$

where $Z$ is the number of atoms per unit cell, $M$ is the molar mass, $a$ is the edge length, and $N_A$ is Avogadro's number.

Rearranging the formula to solve for $Z$:

$Z=\frac{d\times (a^3\times N_A)}{M}$

Substituting the given values $d=2.7$ g cm${}^{-3}$, $M=27$ g mol${}^{-1}$, and $a^3\times N_A=40$ cm${}^3$ mol${}^{-1}$:

$Z=\frac{2.7\times 40}{27}$

$Z=\frac{108}{27}=4$

The number of atoms present in the unit cell is $4$.