This problem provides the molar mass and radius of a metal that has an BCC unit cell and the density is required.
Firstly, we consider the formula that relates molar mass 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 BCC is able to hold 2 atoms and M and NA are given, we calculate the volume of the atom in the unit cell given the radius in meters:
[tex]V=a^3=(\frac{4R}{\sqrt{3} } )^3=(\frac{4*1.74x10^{-10}m}{\sqrt{3} } )^3=6.49x10^{-29}m^3[/tex]
And finally the required density in g/cm³:
[tex]\rho =\frac{2*341.1g/mol}{6.49x10^{-29}m^3\frac{m^3}{atom} *6.022x10^{23}\frac{atom}{mol} } =17455257.8g/m^3\\\\\rho=17.5g/cm^3[/tex]
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