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Question

The length of the unit cell edge of a bcc lattice metal is 350 pm. What is the volume of atoms in one mole of the metal?

A
8.79 cm3
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B
6.25 cm3
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C
1.21 cm3
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D
4.00 cm3
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Solution

The correct option is A 8.79 cm3
In a bcc structure, the atoms touch each other along the body diagonal.
Let,
Radius of an atom =r
AB2=BC2+AC2
BC2=BD2+CD2=a2+a2=2a2
AB2=2a2+a2=3a2
AB=3 a
Also, AB=4r
4r=3 ar=3 a4
r=3×3504 pm
=3×3504×1012 m
=3×3504×1010cm=151.6×1010 cm
Volume of one atom =43πr3=43π(151.6×1010)3cm3=1.46×1023cm3
Volume of N0 atoms is one mole of the metal is
6.02×1023×1.46×1023cm3=8.79 cm3

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