Calculate the density of metal having molar mass $210 \mathrm{~g} \mathrm{~mol}^{-1}$ that forms simple…

Calculate the density of metal having molar mass $210 \mathrm{~g} \mathrm{~mol}^{-1}$ that forms simple cubic unit cell. $\left(\mathrm{a}^3 \cdot \mathrm{N}_{\mathrm{A}}=21.5 \mathrm{~cm}^3 \mathrm{~mol}^{-1}\right)$
  1. $9.77 \mathrm{~g} \mathrm{~cm}^{-3}$
  2. $7.15 \mathrm{~g} \mathrm{~cm}^{-3}$
  3. $8.12 \mathrm{~g} \mathrm{~cm}^{-3}$
  4. $6.94 \mathrm{~g} \mathrm{~cm}^{-3}$

Solution

For simple cubic unit cell, $\mathrm{n}=1$. Density $(\rho)=\frac{\mathrm{nM}}{\mathrm{a}^3 \mathrm{~N}_{\mathrm{A}}}=\frac{1 \times 210}{21.5}=9.77 \mathrm{~g} \mathrm{~cm}^{-3}$

Asked in: MHT CET 2023 (14 May Shift 2)

Practice more Solid State questions on Aicharya