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Question

Iron has an edge length 288pm. Its density is 7.86gmcm1. Find the type of cubic lattice to which the crystal belongs. (Atomic mass of iron = 56).

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Solution

Edge length, a=288pm=2.88×1010cm
Mass of one atom, M=Molar mass of iron NA=566.022×1023
=9.30×1023
Now,
Density, D=n×Ma3
where n= no. of atoms in unit cell
n=7.86×23.89×10236.90×1023
n=2
Thus unit cell contains 2 atoms in it. But bcc crystal structure contains 2 atoms in its unit cell. Hence the crystal structure for iron is body centred cubic structure.

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