Chemistry - Solid State Question with Solution | TestHub

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

$\rho =\frac{\text{Mass of one unit cell}}{\text{Volume of one unit cell}}=\frac{\text{Mass of one unit cell}}{a^3}$

Rearranging this, the mass of one unit cell is:

$\text{Mass of one unit cell}=\rho \times a^3$

Given that $\rho \times a^3=3\times 10^{-22}$ g, this is the mass of a single unit cell.

The total mass of the metal is $0.9$ g. The number of unit cells in the given mass can be calculated as:

$\text{Number of unit cells}=\frac{\text{Total mass}}{\text{Mass of one unit cell}}$

$\text{Number of unit cells}=\frac{0.9}{3\times 10^{-22}}$

$\text{Number of unit cells}=0.3\times 10^{22}=3.0\times 10^{21}$

Answer: $3.0\times 10^{21}$