The density of copper is 8.97 grams per centimeter cubed. What is the radius, in angstroms, of the copper atom ?Atomic weight of Copper = 63.55 g/mol
From copper (8.97g/mL) and its molar mass you can calculate number of Cu atoms in 1mL: N=8.97/63.55*Na, where Na - Avogadro's number. Thus, N=0.85x10^23 atoms/mL. Since copper has cubic face-centered unit cell, it means that there are 4 atoms of Cu per unit cell. If you know the number of atoms in 1mL of Cu, you can calculate the volume of unit cell: V(unit cell)=4/0.85x10^23=4.7058x10^-23mL. Since 1mL=10^24 angstroms, then V(unit cell)=4.7059x10^-23*10^24=47.058 A^3. From unit cell volume you can calculate the cell parameter (the length of the side of unit cell): a=(47.058)^(1/3)=3.6103A. In face-centered unit cells it is assumed that atoms in cell corners and on the cell faces are touching, implying that the length of the face diagonal D will be equal 4*r, where r is atomic radius. Since you know cell parameter, you can calculate D and then r: 2a^2=D^2 => D= a*2^0.5 = 4*r Thus, r=a*(2^0.5)/4 = 1.276A, the radius of Cu atom.
