Calculate Iridium Atom Radius | Material Science

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To calculate the radius of an iridium atom in an FCC crystal structure, begin by using the given density of 22.4 g/cm³ and the atomic weight of 192.2 g/mol. The process involves determining the atomic density by dividing the mass density by the atomic weight and then using Avogadro's number to find the volume of the unit cell. In an FCC structure, there are four atoms per unit cell, which is crucial for relating the unit cell volume to the atomic radius. The edge length of the FCC unit cell is connected to the atomic radius through the face diagonal, which is equal to four times the atomic radius. Understanding these relationships is essential for deriving the atomic radius accurately.
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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!
 
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nebs92 said:
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?
 
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