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Question

A metal (atomic mass =50g) has a body-centered cubic crystal structure. The density of metal is 5.96 g cm3. Find the volume (in cm3) of the unit cell.

A
13.9×1024
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B
27.8×1024
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C
6.95×1024
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D
55.6×1024
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Solution

Correct option: (B)

Analyzing the given data:

Number of atoms in BCC structure =2

Mass of metal =50gmol1

Density of crystal =5.96gcm3

Avogadro number =6.022×1023atoms/mol

Density=Z×MNA×a3

5.96gcm3=2×50g/mol6.022×1023atoms/mol×a3
a3=1006.022×1023×5.96

a3=2.78×1023=27.8×1024cm3
Hence, the volume of the unit cell is 27.8×1024 cm3.


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