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Question

A metal (Atomic mass = 50) has a body centred cubic crystal structure. The density of the metal is 5.96g/cm3. Find the volume of unit cell. (N0=6.023×1023 atoms mol1)

A
2.8×1029cm3
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B
2.8×1023cm3
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C
12.8×1030cm3
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D
14.6×1015cm3
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Solution

The correct option is A 2.8×1023cm3
Density ρ=Z×MN0×a3
ρ=5.96 g/cm3= density
Z=2 atoms= numeber of atoms per unit cell.
M=50 g/mol= atomic weight of metal
N0=6.023×1023 atoms/mol=Avogadro's number
a= edge length
Density ρ=Z×MN0×a3
Density 5.96 g/cm3=2 atoms×50 g/mol6.023×1023 atoms/mol×(a)3
V=a3=2.8×1023 cm3
V is the volume of unit cell.

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