An element (molar mass 180) has BCC crystal structure with density $18 \mathrm{~g} \mathrm{~cm}^{-3}$. What…

An element (molar mass 180) has BCC crystal structure with density $18 \mathrm{~g} \mathrm{~cm}^{-3}$. What is the edge length of unit cell?
  1. $\sqrt[3]{23.2} \times 10^{-24} \mathrm{~cm}$
  2. $\sqrt[3]{12.6} \times 10^{-24} \mathrm{~cm}$
  3. $\sqrt[3]{33.2} \times 10^{-8} \mathrm{~cm}$
  4. $\sqrt[3]{22.6} \times 10^{-8} \mathrm{~cm}$

Solution

$\mathrm{M}=180 \mathrm{~g} \mathrm{~mol}^{-1}, \rho=18 \mathrm{~g} \mathrm{~cm}^{-3} \text {, }$ For BCC crystal, $\mathrm{z}=2, \mathrm{a}=$ ? $\begin{aligned} & \rho=\frac{M \times z}{a^3 \times N_A} \quad \therefore a^3=\frac{M \times z}{\rho \times N_A} \\ & \therefore a^3=\frac{180 \mathrm{~g} \mathrm{~mol}^{-1} \times 2 \text { atom }}{18 \mathrm{~g} \mathrm{~cm}^{-3} \times 6.022 \times 10^{23} \text { atom mol }} \\ & \therefore a^3=33.2 \times 10^{-24} \mathrm{~cm}^3 \\ & \therefore a=\sqrt{33.2} \times 10^{-8} \mathrm{~cm} \end{aligned}$

Asked in: MHT CET 2021 (20 Sep Shift 2)

Practice more Solid State questions on Aicharya