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Question

The density and edge length values for a crystallise elemens with fcc lattice are 10g cm3 and 400 pm, respectively. The number of unit cell in 32g of this crystal is:

A
8×1023
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B
5×1022
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C
8×1022
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D
5×1023
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Solution

The correct option is B 5×1022

Theoretical density of crystal, ρ=nMNoa3 g/cm3

Given that for fcc, n=4, a=400×1010 cm, No=6×1023 ρ=10 g/cm3

M=ρ . No . a3n

=10×6×1023×(400)3×10302

M=96.4 g

Number of moles in 32 g of crystal =3296.4=0.33

Number of atoms =0.33×6.022×1023

Now, in fcc, there are 4 atoms in a unit cell.

So, number of unit cells =0.334×6.022×1023=5×1022


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