Edge length of unit cell of a crystal is $288 \mathrm{pm}$. If its density is $7.2 \mathrm{~g}…

Edge length of unit cell of a crystal is $288 \mathrm{pm}$. If its density is $7.2 \mathrm{~g} \mathrm{~cm}^{-3}$ determine the type of unit cell (cat mass $=52$ ).
  1. Hexagonal cubic
  2. Simple cubic close
  3. Face centered cubic
  4. Body centered cubic

Solution

$d=\frac{Z \times M}{V \times N_A}$ $\begin{aligned} & 7.2=\frac{Z \times 52}{\left(2.88 \times 10^{-8}\right)^3 \times 6.02 \times 10^{23}} \\ & Z=1.991 \simeq 2.0 \end{aligned}$ Therefore, solid has BCC structure.

Asked in: MHT CET 2022 (08 Aug Shift 1)

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