Chemistry: Solid State: Calculation of Density of Unit Cell and Close Packed Structures of Solids (For CBSE, ICSE, IAS, NET, NRA 2022)

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Calculation of Density of Unit Cell

Density =

Volume of unit cell = a3 (if the edge length of cubic unit cell is ‘a’ )

Mass of an atom or molecule = (where M is molar mass of substance,

NA = Avogadro՚s constant)

Atoms or molecules of the substance present/unit cell = Z

Mass of unit cell = (Number of atoms/molecules present/unit cell x mass of one atom/molecule) =

Density =

Close Packed Structures of Solids

  • In the process of the formation of a crystal the constituent particles are closely packed.
  • The crystal structures of the solids are closely packed with identical spheres as shown in figure below.
Close Packed Structures
  • These are held together by forces of attraction.
  • A linear horizontal arrangement of identical spheres in one dimension forms a row.
  • A two-dimensional close packed structure can be obtained by arranging a number of such rows to form a layer.

This can be done in two possible ways they are:

We can align these rows so that each sphere is in contact with four other spheres. This arrangement in two dimensions is called as square close packing.

Two Dimensional Square

We can place the spheres of the second row in the depressions of the first row and so on. In such an arrangement each sphere is in contact with six other spheres. and it is called as hexagonal close packing.

Spheres of the Third Row
  • In hexagonal packing, the spheres of the third row are aligned with the first row and they are packed efficiently.
  • In a hexagonal close packed layer, there are some unoccupied spaces or voids, and these are triangular in shape. It is called as trigonal voids.
  • There are two types of triangular voids, one with the apex pointing upwards and the other with the apex pointing downwards.
Two Types of Triangular Voids

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