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Question

An element crystallizes in a structure having FCC unit cell of an edge 200 pm. Calculate the density if 200 gm of it contains 24×1023 atoms:

A
41.6gm/cm3
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B
42.6gm/cm3
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C
43.6gm/cm3
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D
44.6gm/cm3
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Solution

The correct option is A 41.6gm/cm3

Given,

Edge length=200pm

Number of atoms=24×1023

Given weight of element=200g

Structure of the element = Face centered cubic

In fcc unit cell there are 4 atoms per unit cell.

We know that Density=MassVolume ...(i)

Mass of the unit cell=200×424×1023

33.3×1023g

Volume of the cubic unit cell=(edge)3

(200×1010)3

8×1024cm3

Substituting the value of mass and volume in equation(i), we get

Density=33.3×1023g8×1024cm3

41.6gcm3

Therefore, the density of the element will be 41.6gcm3


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