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

Explanation

Let the , Atomic weight of crystalline substance = M
Avogadro's number = `N_(0)`
No. of atoms present per unit cell = Z
Density of unit cell of the substance = `rho`
Unit cell length = a
So , volume of the unit cell = `a^(3) = (=V)`
`therefore` Then , mass of corresponding to each lattice point = `M//N_(0)`
`therefore ` Mass of Z' lattice points = `(ZM)/(N_(0))`
`therefore` Density `(rho)` of unit cell = `("mass")/("volume") = ((Z.M)/(N_(0)))/(a^(3)) = (ZM)/(N_(0) a^(3))`
Atomic weight `M = (rho xx a^(3) N_(0))/(Z)`