Chemistry - Solid State Question with Solution | TestHub

Formula: The density of a unit cell is $\rho =\frac{Z\cdot M}{N_A\cdot a^3}$, where edge length $a=\frac{4d}{\sqrt{3}}$ and $d$ is the covalent bond length.

Proportionality: Since both diamond and silicon share the same structure ($Z=8$), density simplifies to $\rho \propto \frac{M}{d^3}$.

Ratio Setup: $\frac{density(diamond)}{density(silicon)}=\frac{M_{Carbon}}{M_{Silicon}}\times {\left(\frac{d_{Silicon}}{d_{Carbon}}\right)}^3$

Calculation: Substituting the given table values gives $\frac{12}{28}\times {\left(\frac{2.25}{1.50}\right)}^3=\frac{3}{7}\times (1.5{)}^3=\frac{3}{7}\times 3.375$.

Final Answer: $\frac{81}{56}\approx 1.45$ (or 1.44)