Calculate the density of metal which forms simple cubic structure with edge length of unit cell $336…

Calculate the density of metal which forms simple cubic structure with edge length of unit cell $336 \mathrm{pm}$. (90 gram of meal contains $2.64 \times 10^{23}$ atoms)
  1. $8.98 \mathrm{~g} \mathrm{~cm}^{-3}$
  2. $10.8 \mathrm{~g} \mathrm{~cm}^{-3}$
  3. $7.3 \mathrm{~g} \mathrm{~cm}^{-3}$
  4. $9.46 \mathrm{~g} \mathrm{~cm}^{-3}$

Solution

$\begin{aligned} \mathrm{d} & =\frac{\mathrm{Z} \times \mathrm{M}}{\mathrm{V} \times \mathrm{Na}} \\ & =\frac{1 \times 90}{\left(3.36 \times 10^{-8}\right)^3 \times\left(2.64 \times 10^{23}\right)} \\ & =\frac{90 \times 10}{(3.36)^3 \times 2.64}=8.98 \mathrm{~g} \mathrm{~cm}^{-3}\end{aligned}$

Asked in: MHT CET 2022 (06 Aug Shift 1)

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