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NCERT Class XII Chemistry
Chapter - The Solid State
Questions with Solutions

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Question : 5 of 50
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How can you determine the atomic mass of an unknown metal if you know its density and the dimension of its unit cell? Explain.
Solution:  
Suppose the edge of the unit cell = aa pm
Number of atoms present per unit cell = ZZ
Atomic mass of the element = MM
  \therefore\; Volume of the unit cell =(a±)3=(a \pm)^3
=(a×1010cm)3= (a \times 10^{-10} \mathrm{cm})^{3}
=a3×1030cm3=a^{3} \times 10^{-30} \mathrm{cm}^{3}
Density of the unit cell = Mass of the unit cellVolume of the unit cell\frac{\text{Mass of the unit cell}}{\text{Volume of the unit cell}}
Mass of the unit cell
        \;\;\;\;= Number of atoms in the unit cell × Mass of each atom = Z×mZ \times m
where m=m = mass of each atom
m=Atomic massAvogadro’s number=MN0m=\frac{\text{Atomic mass}}{\text{Avogadro's number}}=\frac{M}{N_{0}}
  \therefore\; Density of the unit cell, ρ=Z×Ma3×N0×1030\rho = \frac{Z \times M}{a^{3} \times N_{0} \times 10^{-30}} gg / cm3\mathrm{cm}^{3}
where edge, a is in pm and molar mass, MM in gg mol1^{-1}.
Atomic mass can be calculated by using the expression
M=ρ×a3×N0×1030Z g mol1M = \frac{\rho \times a^{3} \times N_{0} \times 10^{-30}}{Z} \ \mathrm{g\ mol}^{-1}
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