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Calculation Involving Unit Cell Dimensions

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Calculation Involving Unit Cell Dimensions - Lesson Summary

Calculating the density of the crystal: 
Consider a cubic system with edge length = ‘a’ picometres,
Number of atoms per unit cell =Z,
Molar mass = M.
The volume of a cube =a 3 pm 3
a 3 pm 3 = a 3*10 -30cm 3

Density of a unit cell (ρ) = mass of unit cell / volume of unit cell .-----------------(1)

Mass of a unit cell = number of atoms in the unit cell *mass of each atom
                              =Z*m 
Where m = atomic mass / Avogadro’s number.
                         m=M/N A
                        =Z*M/N A-------------------------------------------------------(2)
Substituting the values in equation 1
                        ρ=Z*m / N A* a 3*10 -30cm 3
Density of a unit cell (ρ) = Z*m / N A* a 3*10 -30
Units=g cm -3

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