Calculate the volume of unit cell if an element having molar mass $92 \mathrm{~g} \mathrm{~mol}^{-1}$ that…

Calculate the volume of unit cell if an element having molar mass $92 \mathrm{~g} \mathrm{~mol}^{-1}$ that forms bcc structure $\left[\varrho \times \mathrm{N}_{\mathrm{A}}=5.0 \times 10^{24} \mathrm{~g} \mathrm{~cm}^{-3} \mathrm{~mol}^{-1}\right]$
  1. $2.44 \times 10^{-23} \mathrm{~cm}^3$
  2. $5.86 \times 10^{-23} \mathrm{~cm}^3$
  3. $3.68 \times 10^{-23} \mathrm{~cm}^3$
  4. $4.76 \times 10^{-23} \mathrm{~cm}^3$.

Solution

For bcc unit cell, $\mathrm{n}=2$. $\text {Density of bec unit cell }=\rho=\frac{M \times n}{a^3 \times N_A}$ $\begin{aligned} \therefore \quad \text { Volume of unit cell }\left(\mathrm{a}^3\right) & =\frac{\mathrm{M} \times \mathrm{n}}{\rho \times \mathrm{N}_{\mathrm{A}}} \\ & =\frac{92 \mathrm{~g} \mathrm{~mol}^{-1} \times 2}{5 \times 10^{24} \mathrm{~g} \mathrm{~cm}^{-3} \mathrm{~mol}^{-1}} \\ & =3.68 \times 10^{-23} \mathrm{~cm}^3\end{aligned}$

Asked in: MHT CET 2024 (10 May Shift 1)

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