Face-centered cubic problems.pdf - Faceu00adcentered cubic...

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1/2/2016 Face­centered cubic problems Face­centered cubic problems Go to a list of only the problems Go to some body­centered cubic problems Go to some general unit cell problems Return to the Liquids & Solids menu Problem #1: Palladium crystallizes in a face­centered cubic unit cell. Its density is 12.023 g/cm 3 . Calculate the atomic radius of palladium.
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2) Calculate the mass of the 4 palladium atoms in the face­centered cubic unit 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:
1/2/2016 Face­centered cubic problems Using the Pythagorean Theorem, we find: d 2 + d 2 = (4r) 2 2d 2 = 16r 2 r 2 = d 2 ÷ 8 r = d ÷ 2(√2) r = 1.3748 x 10¯ 8 cm You may wish to convert the cm value to picometers, the most common measurement used in reporting atomic radii. Try it before looking at the solution to the next problem. Problem #2: Nickel crystallizes in a face­centered cubic lattice. If the density of the metal is 8.908 g/cm 3 , what is the unit cell edge length in pm?
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1) Calculate the average mass of one atom of Ni:
2) Calculate the mass of the 4 nickel atoms in the face­centered cubic unit cell:
3) Use density to get the volume of the unit cell:
4) Determine the edge length of the unit cell:
1/2/2016 Face­centered cubic problems 5) Convert cm to pm: cm = 10¯ 2 m; pm = 10¯ 12 m. Consequently, there are 10 10 pm/cm (3.524 x 10¯ 8 cm) (10 10 pm/cm) = 352.4 pm Problem #3: Nickel has a face­centered cubic structure with an edge length of 352.4 picometers. What is the density? This problem is the exact reverse of problem #2. (See problem 5a below for an example set of calculations.) 2) Calculate the volume of the unit cell
­fcc­AP.html 3/9 3) Calculate the average mass of one atom of Ni 4) Calculate the mass of the 4 nickel atoms in the face­centered cubic unit cell

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