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Question

The density of a unit cell in (g/cm3) can be represented as :
Here,
a is the edge length in pm
Zeff is the effective number of particles in a unit cell
M is the molar mass NA is the avogadro number

A
MNA×a3×1030×Zeff
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B
Zeff×MNA×a3×1030
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C
NA×a3×1030Zeff×M
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D
NA×a3×1030×ZeffM
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Solution

The correct option is B Zeff×MNA×a3×1030
Density of a Unit Cell:
It is the ratio of total mass of particles present and volume of a unit cell.
Density of the unit cell=Total mass of particles in the unit cell Volume of the unit cell

Mass of a unit cell is the total mass of effective number of particles present in a unit cell.
Mass of a unit cell=Number of particles in a unit cell ×Mass of one particle
Mass of one particle=Molar Mass (M) Avogadro number (NA)



The volume of a unit cell of a cubic lattice is :
Vc=a3×1030 cm3

Density (ρ)=(Number of particles in a unit cell) ×(Molar mass)(Volume of unit cell) ×NA

Density (ρ)=Zeff×MNA×a3×1030 g cm3

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