A metal has BCC structure with edge length of unit cell $400 \mathrm{pm}$. Density of metal is $4…

A metal has BCC structure with edge length of unit cell $400 \mathrm{pm}$. Density of metal is $4 \mathrm{~g} \mathrm{~cm}^{-3}$ What is molar mass of metal?
  1. $40 \mathrm{~g} \mathrm{~mol}^{-1}$
  2. $27 \mathrm{~g} \mathrm{~mol}^{-1}$
  3. $92 \mathrm{~g} \mathrm{~mol}^{-1}$
  4. $77 \mathrm{~g} \mathrm{~mol}^{-1}$

Solution

$\begin{aligned} & \mathrm{d}=\frac{\mathrm{ZM}}{\mathrm{N}_{\mathrm{A}} \cdot \mathrm{a}^3} \\ & \mathrm{a}=400 \mathrm{pm} \\ & =400 \times 10^{-10} \mathrm{~cm} \\ & =4 \times 10^{-8} \mathrm{~cm} \\ & \mathrm{Z}=2 \text { for BCC } \\ & 4=\frac{2 \times \mathrm{M}}{6.022 \times 10^{23} \times\left(4 \times 10^{-8}\right)^3} \\ & \mathrm{M}=\frac{4 \times 6.022 \times 10^{23} \times 64 \times 10^{-24}}{2} \\ & =77 \mathrm{~g} \mathrm{~mol}^{-1}\end{aligned}$

Asked in: MHT CET 2021 (23 Sep Shift 1)

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