Calculate Iridium Atom Radius | Material Science

[nebs92]

Hi I am in a material science class and one of my homework questions states:

"Calculate the radius of an iridium atom,given that Ir has an FCC crystal structure, a density of 22.4g/cm^3,and an atomic weight of 192.2g/mol."

I think I have to use the Pythagorean theorem somewhere but my teacher went off on some tangent about something unrelated when he was talking about this. Any help will be greatly thanked!

 

[Astronuc]

Hi I am in a material science class and one of my homework questions states:

"Calculate the radius of an iridium atom, given that Ir has an FCC crystal structure, a density of 22.4g/cm^3,and an atomic weight of 192.2g/mol."

I think I have to use the Pythagorean theorem somewhere but my teacher went off on some tangent about something unrelated when he was talking about this. Any help will be greatly thanked!

One uses the mass density and the atomic weight to determine the atomic density. Dividing by Avogadro's (or Loschmidt's) number, one obtains the volume of a metals unit cell, then one must relate this to the number of atoms in the unit (crystal) cell and the cell dimensions to the atomic radius or diameter. It's relatively simple and straightforward for cubic structures.

How many atoms in an FCC cell?

What is the relationship of the length of the cell edge or lattice parameter to the atomic radius on an FCC metal?

Or what is significant about the face diagonal of the FCC cell?

Similar, what is significant about the major diagonal (opposite corner, not the same face) for a bcc cell?