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

Let d=density of the unit cell and volume of the unit cell =$a^3$(in case of cubic crystal)
Mass of an atom present in the unit cell
$m=\large\frac{M}{N_A}$
m=Molar mass
Therefore,density of the unit cell=$\large\frac{\text{Mass of unit cell}}{\text{Volume of unit cell}}$
$d=\large\frac{z\times M}{a^3\times N_A}$
By this formula we can calculate
$M=\large\frac{d\times a^3\times N_A}{z}$
Where $z\rightarrow$ No of atoms in unit cell,$N_A\rightarrow$ Avagadro number