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Question

An element A crystallises in a fcc structure. 200 g of this element has 4.12×1024 atoms. The density of A is 7.2 g cm3. Calculate the edge length of the unit cell.

A
26.97×1024 cm
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B
299.9 pm
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C
5×1012 cm
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D
2.99 cm
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Solution

The correct option is C 299.9 pm
A fcc unit cell has 4 atoms.

200 g corresponds to 4.12×1024 atoms.

Hence, 4 atoms corresponds to 200×44.12×1024 g.

Density=MassVolume

Substituting values in the above expression, we get

7.2=200×44.12×1024×a3

Hence, a=299.9×1010 cm =299.9 pm

Hence, the edge length of the unit cell is 299.9 pm.

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