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.
volume of a sphere = (4/3)*pi*r3.
400 nm = 400 x 10^-9 m. I would convert to cm so that the answer will come out in cc. Note that 400 nm is NOT 400 Angstroms.
but 400nm is the radius of the gold particle not the atom. Pls help!!
To determine the volume of each gold atom in the given gold particle, we need to know the formula for calculating the volume of a sphere. The formula for the volume of a sphere is given by:
V = (4/3)πr^3
where V is the volume and r is the radius of the sphere.
In this case, we are given the radius of the gold particle as 400 nm (nanometers). However, we need to convert this radius into angstroms (Å) because the FCC structure is typically described in units of angstroms.
To convert nanometers to angstroms, we need to remember that 1 nm is equal to 10 angstroms. So, the radius of the gold particle in angstroms is:
400 nm * 10 = 4000 Å
Now that we have the radius in angstroms, we can substitute this value into the formula for the volume of a sphere to calculate the volume of each gold atom.
V = (4/3) * π * (4000 Å)^3
Calculating this expression will give us the volume of each gold atom in cubic angstroms (Å^3).
Let's now calculate the volume of each gold atom using the provided information.