What is molar mas of metal with BCC structure having density $10 \mathrm{~g} \mathrm{~cm}^{-3}$ and edge…

What is molar mas of metal with BCC structure having density $10 \mathrm{~g} \mathrm{~cm}^{-3}$ and edge length $200 \mathrm{pm}$ ?
  1. $90.2 \mathrm{~g} \mathrm{~mol}^{-1}$
  2. $24 \mathrm{~g} \mathrm{~mol}^{-1}$
  3. $48.0 \mathrm{~g} \mathrm{~mol}^{-1}$
  4. $60.5 \mathrm{~g} \mathrm{~mol}^{-1}$

Solution

BCC structure, $\mathrm{Z}=2$ (Number of atoms in one unit cell) $\begin{aligned} & \mathrm{d}=\frac{\mathrm{Z} \cdot \mathrm{M}}{\mathrm{N}_{\mathrm{A}} \cdot \mathrm{a}^3} \\ & \mathrm{a}=200 \mathrm{pm}=200 \times 10^{-10} \mathrm{~cm} \text { or } 2 \times 10^{-8} \mathrm{~cm} \\ & 10=\frac{2 \times \mathrm{M}}{6 \times 10^{23} \times\left(2 \times 10^{-8}\right)^3} \\ & 10=\frac{2 \times \mathrm{M}}{6 \times 10^{23} \times 8 \times 10^{-24}} \\ & \mathrm{M}=\frac{10 \times 6 \times 10^{23} \times 10^{-24} \times 8}{2} \\ & =24 \mathrm{~g} / \mathrm{mol} \end{aligned}$

Asked in: MHT CET 2021 (20 Sep Shift 1)

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