What is atomic mass of an element with $\mathrm{BCC}$ structure and density $10 \mathrm{~g}…

What is atomic mass of an element with $\mathrm{BCC}$ structure and density $10 \mathrm{~g} \mathrm{~cm}^{-3}$ having edge length $300 \mathrm{pm}$ ?
  1. $51.0 \mathrm{~g} \mathrm{~mol}^{-1}$
  2. $60.0 \mathrm{~g} \mathrm{~mol}^{-1}$
  3. $81.3 \mathrm{~g} \mathrm{~mol}^{-1}$
  4. $96.8 \mathrm{~g} \mathrm{~mol}^{-1}$

Solution

For bcc unit cell, $\mathrm{n}=2$. $\begin{aligned} & \text { Density of bcc unit cell }=\rho=\frac{\mathrm{Mn}}{\mathrm{a}^3 \mathrm{~N}_{\mathrm{A}}} \\ & \mathrm{M}=\frac{\rho \times \mathrm{a}^3 \times \mathrm{N}_{\mathrm{A}}}{\mathrm{n}} \\ & \mathrm{M}=\frac{10 \mathrm{~g} \mathrm{~cm}^{-3} \times\left(3 \times 10^{-8} \mathrm{~cm}\right)^3 \times 6.022 \times 10^{23} \mathrm{atom} \mathrm{mol}^{-1}}{2 \text { atoms }} \\ & \mathrm{M}=81.3 \mathrm{~g} \mathrm{~mol}^{-1} \end{aligned}$

Asked in: MHT CET 2023 (11 May Shift 1)

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