Volume of an iron atom question.?

Question

Iron has a mass of 7.87 g per cubic centimeter of volume, and the mass of an iron atom is 9.27 x 10^-26 kg. If the atoms are spherical and tightly packed, (a) what is the volume of an iron atom and (b) what is the distance between the centers of adjacent atoms?

The answer for (a) is 1.18 x 10^-29 m^3. I am not sure about (b). Could you please show me the steps in solving both (a) and (b)?

Answer 1

Tight packing of spherical objects implies a regular lattice structure. Answer A is just mass/density, and refers to the average volume, including empty space, per atom. We want to find the volume of the spherical atom; then we can derive the radius r, and the center-to-center separation is just 2r. Per the ref., the maximum packing efficiency is 0.7405. Then we can say that the atom-only volume is 1.18E-29*0.7405 m^3. You can take it from there.