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The Solid State

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Chemistry I

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Chemistry

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CBSE Gujarat Board Haryana Board

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Class 10 Class 12
An element crystallizes in a structure having a fcc unit cell of an edge 200 pm. Calculate its density if 200 g of this element contains 24 x 1023 atoms.

Solution:
We have given that
Edge length of the unit cell
= 200 pm = 200 x 10–10 cm

Vol. of the unit cell
= (200 x 10–10 cm)= 8 x 10–24 cm3
Therefore, volume of the substance
= Vol. of unit cell x Vol. of 1 unit cell.

Since the element has a fcc unit cell, number of atoms per unit cell = 4.
Total number of atoms = Atoms/unit cell x number of unit cells.
                                     = 24 x 1023atoms = 4

atoms/unit cell x No. of unit cells.

∴   No. of unit cells = 24×1023 atoms4 atoms/unit cell

                               = 6×1023 unit cells.

∴  Volume of the substance
                   6×1023 unit cell × 8× 10-24 cm3/unit cell = 4.8 cm3


Now,     Density  = MassVolume               = 200g4.8 cm3 =4.17 g cm-3.



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