A certain metal alloy has a packing factor of 0.64,an average atomic mass of 67.

Question

A certain metal alloy has a packing factor of 0.64,an average atomic mass of 67.15 amu, and an average atomic radiusof 0.157nm. Determine the theoretical density of this alloy, ing/cm3, based on one cubic centimeter ofmetal.

Explanation / Answer

volume of atom in 1 cm3 => packing factor*1 cm3 = 0.67 cm3 volume of atom = (4/3)r3 = (4/3)*(0.157 nm*1e2 cm/1e9 nm)3 = 1.62101699e-23 cm3 number of atoms = 0.57 cm3 *( 1atom/1.62101699e-23 cm3) =3.51631108e22 atoms 3.51631108e22 atoms *(67.15 amu /atom) *(1 g / 6.022e23 amu) = 3.92grams 3.92 grams per cm3 => density => 3.92 g/cm3

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