Calculate the number of atoms in 20 gram metal which crystalises to simple cubic structure having unit cell…

Calculate the number of atoms in 20 gram metal which crystalises to simple cubic structure having unit cell length $340 \mathrm{pm}$. (density of metal $=9.8 \mathrm{~g} \mathrm{~cm}^{-3}$ )
  1. $5.81 \times 10^{22}$
  2. $5.19 \times 10^{22}$
  3. $5.42 \times 10^{22}$
  4. $4.95 \times 10^{22}$

Solution

$\mathrm{d}=\frac{\mathrm{Z} \times \mathrm{M}}{\mathrm{V} \times \mathrm{N}_{\mathrm{A}}}$ $9.8=\frac{1 \times M}{\left(3.40 \times 10^{-8}\right)^3 \times 6.02 \times 10^{23}}$ $\begin{aligned} & M=\frac{9.8 \times 6.02 \times 39.3}{10} \\ & =231.87\end{aligned}$ Moles of atom in $20 \mathrm{~g}$ sample $=\frac{20}{231.87}=0.08625$ No. of atoms $=0.08625 \times 6.02 \times 10^{23}$ $=5.19 \times 10^{22}$

Asked in: MHT CET 2022 (05 Aug Shift 1)

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