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

Explanation

Suppose edge length of cubic unit cell = a pm
Density of solid = d
Let number of atoms present per unit cell = Z
Suppose M is the molar mass of the metal.
Mass of one atom of the metal, `m=M/(N_(A))`
where `N_(A)="Avogadro.s number"(6.022xx10^(23))`
Density of unit cell, `d=("Mass of unit cell")/("Volume of unit cell")=(zxxm)/(a^(3))`
`d=(Z*M)/(a^(3)N_(A))orM=(d*a^(3)*N_(A))/(Z)`
Thus, knowing d (density), a (edge length) and z (number of atoms present per unit cell), molar mass M (or atomic mass) of the meal can be calculated.