The density of chromium metal is $7 \mathrm{~g} \mathrm{~cm}^{-3}$. If edge length of unit cell is $300…

The density of chromium metal is $7 \mathrm{~g} \mathrm{~cm}^{-3}$. If edge length of unit cell is $300 \mathrm{pm}$, identify the type of unit cell. (At. mass $\mathrm{Cr}=52$ )
  1. Body centred cubic
  2. Simple cubic
  3. Hexagonal close pack
  4. Face centred cubic

Solution

$\begin{aligned} & \mathrm{d}=\frac{\mathrm{ZM}}{\mathrm{N}_{\mathrm{A}} \mathrm{a}^3} \\ & \mathrm{Z}=\frac{\mathrm{d} \cdot \mathrm{N}_{\mathrm{A}} \cdot \mathrm{a}^3}{\mathrm{M}} \\ & \mathrm{a}=300 \mathrm{pm} \\ & \mathrm{a}=300 \times 10^{-10} \mathrm{~cm} \\ & \mathrm{a}=3 \times 10^{-8} \mathrm{~cm} \\ & =\frac{7 \times 6.022 \times 10^{23} \times\left(3 \times 10^{-8}\right)^3}{52} \end{aligned}$ Unit cell is Body centred cubic

Asked in: MHT CET 2021 (24 Sep Shift 2)

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