Derivation

Mass of unit cell: Each atom has mass = M/Nₐ (molar mass / Avogadro's number). Unit cell contains Z atoms.

$\text{Mass} = Z \times \frac{M}{N_A}$

Volume of unit cell: $V = a^3 \text{ (for cubic)}$

Density: $\boxed{\rho = \frac{Z \cdot M}{a^3 \cdot N_A}}$

Dimensional check: \frac{\text{(dimensionless)} \times (g \cdot $mol^{-1}$)}{(cm^3) \times ($mol^{-1}$)} = \frac{g \cdot $mol^{-1}$}{cm^3 \cdot $mol^{-1}$} = g \cdot $cm^{-3}$ \checkmark

Unit Conversions (Critical for NEET)

• 1 Å = 10^{-8} cm = 10^{-10} m = 100 pm
• 1 pm = 10^{-10} cm

Rearrangements