﻿ 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. from Chemistry The Solid State Class 12 Nagaland Board

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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 =

∴  Volume of the substance

Now,

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