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

Explanation

Consider a unit cell with edge length `= a pm = 10^(-10) cm`
volume of the unit cell ` = (a xx 10^(-10))^(3) = a^(3) xx 10^(-30) cm^(3)`
Density of unit cell `= ("Mass of unit cell")/("Volume of unit cell")`
Now, mass of unit cell
= Number of atoms in a unit cell `xx` Mass of each atoms
`= (Z_(eff) xx "Atomic mass" (Aw))/("Avogadro's number"(N_(A))`
By substituting the value of mass of unit cell in Eq.
Density of the unit cell `= (Z_(eff) xx Aw)/(N_(A) xx (a^(3) xx 10^(-30) cm^(3))`
`= (Z_(eff) xx Aw)/(N_(A) xx a^(3) xx 10^(-30)) (g cm^(-3))`
From the above formula, we can calculate the atomic mass `(Aw)` of an unknown metal.