# roblem.docx - problem #1: Palladium crystallizes in a...

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problem #1:Palladium crystallizes in a face-centered cubic unit cell. Itsdensity is 12.023 g/cm3. Calculate the atomic radius of palladium.Solution:
2) Calculate the mass of the 4 palladium atoms in the face-centered cubicunit cell:
3) Use density to get the volume of the unit cell:
4) Determine the edge length of the unit cell:
5) Determine the atomic radius:
Using the Pythagorean Theorem, we find:d2+ d2= (4r)22d2= 16r2r2= d2÷ 8r = d ÷ 2(√2)r = 1.3748 x 10¯8cmYou may wish to convert the cm value to pedometers, the most commonmeasurement used in reporting atomic radii. Try it before looking at thesolution to the next problem.Problem #2:Nickel crystallizes in a face-centered cubic lattice. If thedensity of the metal is 8.908 g/cm3, what is the unit cell edge length in pm?
1) Calculate the average mass of one atom of Ni:
2) Calculate the mass of the 4 nickel atoms in the face-centered cubic unitcell:
3) Use density to get the volume of the unit cell:
4) Determine the edge length of the unit cell:
5) Convert cm to pm:
Problem #3:Nickel has a face-centered cubic structure with an edge lengthof 352.4 pedometers. What is the density?This problem is the exact reverse of problem #2. (See problem 5a below foran example set of calculations.)2) Calculate the volume of the unit cell
3) Calculate the average mass of one atom of Ni4) Calculate the mass of the 4 nickel atoms in the face-centered cubic unitcell5) Calculate the density (value from step 4 divided by value from step 2)Problem #4:Calcium has a cubic closest packed structure as a solid.

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Term
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Tags
Atom, Cubic crystal system, Avogadro constant, Use density