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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/cm3Given, 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 ⇒33.3×10−23g Volume of the cubic unit cell=(edge)3 ⇒(200×10−10)3 ⇒8×10−24cm3 Substituting the value of mass and volume in equation(i), we get Density=33.3×10−23g8×10−24cm3 ⇒41.6gcm−3 Therefore, the density of the element will be 41.6gcm−3

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