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Question

The number of atoms in 100 g of an fcc crystal with density =10.0 gcm3 and cell edge equal to 200 pm is equal to:

A
5×1024
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B
5×1025
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C
6×1023
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D
2×1025
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Solution

The correct option is A 5×1024

d=Z×Ma3×NA


where a is the edge of a unit cell


NA = Avogadro number (6.022×1023)


M = Molar mass


Z = number of atoms per unit cell


For FCC,


Z=4


From the given data, we can calculate the molar mass of the given substance as:


M=d×a3×NAZ


​Number of atoms = Given massmolar mass(M)×NA


Putting the value of M in the above equation we get-


Number of atoms =Given mass×Z×NAd×a3×NA


Number of atoms =Given mass×Zd×a3


Putting the values we get:

Number of atoms=100×410×(200×1010)3


=5×1024atoms

Hence, option A is correct.


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