Question

The density of a unit cell $\text{in}\left(g/c{m}^3\right)$ can be represented as :
Here,
$a\text{is the edge length in}pm$
$Z_{eff}\text{is the effective number of particles in a unit cell}$
$M\text{is the molar mass}{N}_A\text{is the avogadro number}$

• A. $\frac{M}{N_A\times a^3\times {10}^{-30}\times Z_{eff}}$
• B. $\frac{Z_{eff}\times M}{N_A\times a^3\times {10}^{-30}}$
• C. $\frac{N_A\times a^3\times {10}^{-30}}{Z_{eff}\times M}$
• D. $\frac{N_A\times a^3\times {10}^{-30}\times Z_{eff}}{M}$

Answer 1

The correct option is B $\frac{Z_{eff}\times M}{N_A\times a^3\times {10}^{-30}}$

Density of a Unit Cell:
It is the ratio of total mass of particles present and volume of a unit cell.
$\text{Density of the unit cell}=\frac{\text{Total mass of particles in the unit cell}}{\text{Volume of the unit cell}}$

Mass of a unit cell is the total mass of effective number of particles present in a unit cell.
$\text{Mass of a unit cell}=\text{Number of particles in a unit cell}\times \text{Mass of one particle}$
$\text{Mass of one particle}=\frac{\text{Molar Mass (M)}}{\text{Avogadro number}\left(N_A\right)}$



The volume of a unit cell of a cubic lattice is :
$V_c=a^3\times {10}^{-30}c{m}^3$

$\text{Density}\left(\rho \right)=\frac{\text{(Number of particles in a unit cell)}\times \text{(Molar mass)}}{\text{(Volume of unit cell)}\times N_A}$

$\text{Density}\left(\rho \right)=\frac{Z_{eff}\times M}{N_A\times a^3\times {10}^{-30}}gc{m}^{-3}$