Class 12 Chemistry The Solid State Number of atoms per unit cell in Face Centered Cubic Unit Ce

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.

 

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