How can you determine the atomic mass of an unknown metal if you know its density and the dimension of its unit cell? Explain.

(N/A) By knowing the density of an unknown metal and the dimension of its unit cell,the atomic mass of the metal can be determined.
Let $a$ be the edge length of a unit cell of a crystal,$d$ be the density of the metal,$M$ be the atomic mass of the metal,$z$ be the number of atoms in the unit cell,and $N_{A}$ be Avogadro's number.
The density of the unit cell is given by:
$d = \frac{z \times M}{a^{3} \times N_{A}}$
Rearranging the formula to solve for the atomic mass $(M)$:
$M = \frac{d \times a^{3} \times N_{A}}{z}$
By substituting the known values of density $(d)$,edge length $(a)$,Avogadro's number $(N_{A})$,and the number of atoms per unit cell $(z)$ based on the crystal structure (e.g.,$z=1$ for simple cubic,$z=2$ for $BCC$,$z=4$ for $FCC$),the atomic mass $(M)$ can be calculated.