Calculate the number of atoms present in unit cell of an element having molar mass $190 \mathrm{~g}…

Calculate the number of atoms present in unit cell of an element having molar mass $190 \mathrm{~g} \mathrm{~mol}^{-1}$ and density $20 \mathrm{~g} \mathrm{~cm}^{-3}$. $\left[\mathrm{a}^3 \cdot \mathrm{N}_{\mathrm{A}}=38 \mathrm{~cm}^3 \mathrm{~mol}^{-1}\right]$
  1. $1$
  2. $2$
  3. $6$
  4. $4$

Solution

Density $(\rho)=\frac{M \mathrm{n}}{\mathrm{a}^3 \mathrm{~N}_{\mathrm{A}}}$ $\begin{aligned} & 20=\frac{190 \times \mathrm{n}}{38} \\ & \mathrm{n}=\frac{20 \times 38}{190}=4 \end{aligned}$

Asked in: MHT CET 2023 (10 May Shift 2)

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