Hi guys, i get stuck with this question. Pls help. thanks so much. I know there are 4 atoms in FCC.

A gold particle was measured to be spherical in shape with a radius of 400 nm. Note that assuming the gold atoms are small spheres that form the gold particle by packing together in a Face-Centered Cubic (FCC) structure. Determine the volume of each gold atom. Note that here A = Angstrom.

I don't understand what is meant by a gold "particle". Why not a large nugget of radius 2cm? What does that have to do with packing and cell size?

yeah i also don't know that. as stated in the question, the gold atoms form the gold particle. Thanks

To determine the volume of each gold atom in a FCC structure, we can start by calculating the volume of the gold particle using its radius.

The formula for the volume of a sphere is given by:
V = (4/3) * π * r^3

Given that the radius of the gold particle is 400 nm (nanometers), we need to convert it to Angstroms (A) since the measurement for the volume of each atom is given in Angstroms.

1 nm (nanometer) = 10 A (Angstrom)

So, the radius in Angstroms would be:
400 nm * 10 A/nm = 4000 A

Now we can calculate the volume of the gold particle:
V_particle = (4/3) * π * (4000 A)^3

Next, we need to determine the number of gold atoms in the FCC structure. In a FCC structure, there are 4 atoms per unit cell.

So, the volume occupied by each gold atom, V_atom, within the FCC structure is given by:
V_atom = V_particle / (number of atoms per unit cell)

V_atom = V_particle / 4

Finally, we can calculate the volume of each gold atom by substituting the value of V_particle into the formula:
V_atom = [(4/3) * π * (4000 A)^3] / 4

Evaluating this expression will give you the volume of each gold atom in Angstroms cubed (A^3).