[ride5150]

for copper, the atomic radius is 128nm, i have used the formula N=((Avogadros number)(Density))/(Atomic Wt) to find that the number of atomic sites per meter cubed is about 8.5 X 10^28.

How would i calculate atomic sites/meter cubed by just knowing the atomic radius of copper?

i have taken the volume of 1m cubed divided by the volume of a FCC unit cell of copper, returning the number of unit cells in a cubic meter. then multiplied this number by the number of atoms in a FCC unit cell, which is 4. this hasnt given me the same answer as calculated before, 8.5X10^28.

more specifically, this is what i did:

Volume of 1 FCC Copper Unit Cell= (16)((128X10^-9m)^3)(SqrRt(2))=            4.75*10^-20m Cubed

(1m Cubed)/(4.75*10^-20m Cubed)=  2.11*10^19 Unit Cells in 1 m Cubed

1 FCC Unit cell has 4 atoms.

(2.11*10^19 Unit Cells in 1 m Cubed)(4 Atoms per FCC Unit Cell)=     8.43*10^19 atoms in 1m cubed?

thats not what i got by calculating number of atomic sites using the equation: N=((Avogadros number)(Density))/(Atomic Wt)
= [(6.022*10^23)(8.95g/cm Cubed)(10^6cm Cubed/ meter Cubed)]/(63.55g/mol) = 8.5*10^28 Atomic Sites / meter Cubed

what am i doing wrong? help?

[Borek]

There is a free space between atoms, so you can't assume they occupy whole volume.

[cth]

There is only one problem in what you did: copper atomic radius is not 128nm, but it is 128pm.

Otherwise, everything else you did looks OK to me.

You did take into account the free space inside the unit cell when doing the following:

Volume of 1 FCC Copper Unit Cell= (16)((128X10^-9m)^3)(SqrRt(2))=            4.75*10^-20m Cubed

Which derives from the atoms touching along the face diagonals of the FCC cube:
a*(sqrRT(2))=4R  --->  a=2*(sqrRT(2))*R
with R: radius of copper atoms
       a: side length of the cubic unit cell
Then
volume of the unit cell: a³=(2*(sqrRT(2))*R)³
                                 a³=16*R³*(sqrRT(2))   as you found

Well done  . Just watch for the unit mistake on the atomic radius: picometer, not nanometer. It is easy to do avoid it.

[Borek]

My mistake, I misunderstood the original post.

[ride5150]

ahh picometers...thanks i kept on thinking it was nanometers:P well im glad at least my logic was correct