A metal crystallises in bcc structure with edge length $4 \times 10^{-8}$. If density of unit cell is $10…

A metal crystallises in bcc structure with edge length $4 \times 10^{-8}$. If density of unit cell is $10 \mathrm{~g} \mathrm{~cm}^{-3}$. What is its molar mass?
  1. $60 \mathrm{~g} \mathrm{~mol}^{-1}$
  2. $152 \mathrm{~g} \mathrm{~mol}^{-1}$
  3. $120 \mathrm{~g} \mathrm{~mol}^{-1}$
  4. $193 \mathrm{~g} \mathrm{~mol}^{-1}$

Solution

For bec unit cell, $\mathrm{n}=2$. $\begin{aligned} & \text { Density }(\rho)=\frac{M \times n}{\mathrm{a}^3 \mathrm{~N}_{\mathrm{A}}} \\ & 10 \mathrm{~g} \mathrm{~cm}^{-3}=\frac{\mathrm{M} \times 2}{\left(4 \times 10^{-8} \mathrm{~cm}\right)^3 \times 6.022 \times 10^{23} \mathrm{~mol}^{-1}} \\ & \mathrm{M}=\frac{6.022 \times 10^{23} \mathrm{~mol}^{-1} \times\left(4 \times 10^{-8} \mathrm{~cm}^3 \times 10 \mathrm{~g} \mathrm{~cm}^{-3}\right.}{2} \\ \therefore \quad & M=193 \mathrm{~g} \mathrm{~mol}^{-1} \end{aligned}$

Asked in: MHT CET 2024 (11 May Shift 2)

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