What is the density of an element (At. mass $100 \mathrm{~g} \mathrm{~mol}^{-1}$ ) having BCC structure with…

What is the density of an element (At. mass $100 \mathrm{~g} \mathrm{~mol}^{-1}$ ) having BCC structure with edge length $400 \mathrm{pm}$ ?
  1. $3.2 \mathrm{~g} \mathrm{~cm}^{-3}$
  2. $8.2 \mathrm{~g} \mathrm{~cm}^{-3}$
  3. $5.18 \mathrm{~g} \mathrm{~cm}^{-3}$
  4. $4.8 \mathrm{~g} \mathrm{~cm}^{-3}$

Solution

$\begin{aligned} & \mathrm{a}=400 \mathrm{pm}=400 \times 10^{-12} \mathrm{~m} \\ & =400 \times 10^{-10} \mathrm{~cm} \\ & =4 \times 10^{-8} \mathrm{~cm} \\ & \mathrm{Z}=2(\text { for } \mathrm{BCC}) \\ & \mathrm{d}=\frac{\mathrm{Z} \times \mathrm{M}}{\mathrm{N}_{\mathrm{A}} \cdot \mathrm{a}^3}=\frac{2 \times 100}{6.022 \times 10^{23} \times\left(4 \times 10^{-8}\right)^3}=5.18 \mathrm{~g} \mathrm{~cm}^{-3}\end{aligned}$

Asked in: MHT CET 2021 (21 Sep Shift 2)

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