This problem provides the molar mass and radius of a metal that has an FCC unit cell and the density is required.
Firstly, we begin with the formula that relates the aforementioned variables and also includes the Avogadro's number and the volume of the unit cell:
[tex]\rho=\frac{Z*M}{V*N_A}[/tex]
Whereas Z stands for the number of atoms in the unit cell, M the molar mass, V the volume and NA the Avogadro's number. Next, since FFC is able to hold 4 atoms and M and NA are given. Next, we calculate the volume of the atom in the unit given the radius in meters:
[tex]V=a^3=(2*1.92x10^-10m*\sqrt{2} )^3=1.60x10^{-28}m^3/atom[/tex]
And finally the required density in g/cm³:
[tex]\rho=\frac{4*241.5g/mol}{1.60x10^{-28}m^3/atom*6.022x10^{23}atom/mol} \\\\\rho=10025739g/m^3=10.03 g/cm^3[/tex]
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