Question

Inorganic Chemistry: Show that the atoms occupy only 52.4% of the total volume in a primitive or simple cubic unit cell.(By contrast, in a closest-packed structure like fcc, the atoms occupy 74% of the total volume)

Answer #1

In a primitive or simple cubic unit cell, the atoms are located at the corners of unit cell such that the adjacent atoms touch each other. Thus, radius of atom becomes (a/2).

Each atom is shared by eight cubes, hence, one eighth of each atom is in the cube. Therefore, total number of atoms in a cube = 1/8 x 8 = 1 atom.

Expression for total volume occupied by atom in a unit cell can be given as follows:

Volume of atom / volume of cell = (4/3 πr^{3})/
a^{3}

Where, r = radius of atom = a/2

a = length of a side of cube

Therefore, Volume of atom / volume of cell = [4/3 π
(a/2)^{3}]/ a^{3}

Volume of atom / volume of cell = π/6

Volume of atom / volume of cell = 3.142/6

Volume of atom / volume of cell = 0.524

Thus, if volume of cell is 100 then volume of atom will be 52.4.
Alternatively, **52.4% of total volume in
primitive or simple cubic unit cell is occupied by an
atom**.

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lattice constant of 0.287 nm:
a. Use drawing to show how the iron atoms are packed in the unit
cell. How many iron atoms are contained in each unit
cell?
b. Use drawings to show how the iron atoms are arranged on the
(100) and (110)
planes.
c. Determine diameter of iron atom
d. Determine the density of iron (g/cm3) by dividing
the total mass of iron atoms in...

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lattice constant of 0.287 nm:
a. Use drawing to show how the iron atoms are packed in the unit
cell. How many iron atoms are contained in each unit
cell?
b. Use drawings to show how the iron atoms are arranged on the
(100) and (110)
planes.
c. Determine diameter of iron atom
d. Determine the density of iron (g/cm3) by dividing
the total mass of iron atoms in...

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