Number of atoms per unit cell : Face Centered Cubic Unit Cell
- In a face-centered cubic (fcc) unit cell the atoms are present in the corners and at the center of all the faces of the cube.
- Each atom present at the face-center is shared between two adjacent unit cells and only a ½ of each atom belongs to a unit cell.
Thus, in a face-centered cubic (fcc) unit cell:
8 corners X 1/8 per corner atom = 8 * 1/8 = 1 atom
6 face-centered atoms X 1/2 per unit cell = 6 X 1/2 = 3 atoms
Total number of atoms per unit cell = 4 atoms
In solids, these constituent particles are closely-packed that leaves minimum vacant space.
Question : An element with molar mass 2.7×10-2kg mol-1 forms a cubic unit cell with edge length 405 pm. If its density is 2.7×103kg-3, what is the nature of the cubic unit cell?
Answer : d = 2.7×103kg-3
M = 2.7×10 -2 kg mol-1
a= 405 pm = 405 X 10-12
NA= 6.023 X 1023
Using the formula
Z=4
Unit cell is fcc unit cell.
Volume of 54 g of the element = 0.054/(2.7X103) = 2 X 10-6
Number of unit cell in this volume = volume of 554 g of element/volume of each unit cell = 2 X 10-6/(405 X 10-12)3 = 3.012 X 1022
Question: Copper crystallises into a fcc lattice with edge length 3.61 x 10-8cm. Show that the calculated density is in agreement with its measured value of 8.92 g cm-3
Answer: Given that Copper crystallises into a fcc lattice
Hence Z= 4
M = 63.5
a = 3.61x10-8
No = 6.023 x 1023
Using the formula
Therefore, approximately the value is equal to 8.92.
