Unit cell of an element has edge length of $5 Å$ with density $4 \mathrm{~g} \mathrm{~cm}^{-3}$, if its…

Unit cell of an element has edge length of $5 Å$ with density $4 \mathrm{~g} \mathrm{~cm}^{-3}$, if its atomic mass is 149 , identify the crystal structure.
  1. Simple cubic close packed
  2. Body centred cubic
  3. Face centred cubic
  4. Hexagonal close packed

Solution

$\begin{aligned} & \text {Density }(\rho)=\frac{n \times M}{a^3 \times N_A} \\ \therefore \quad & n=\frac{\rho N_A a^3}{M} \\ & =\frac{4 \mathrm{gcm}^{-3} \times 6.022 \times 10^{23} \mathrm{~mol}^{-1} \times\left(5 \times 10^{-8} \mathrm{~cm}\right)^3}{149 \mathrm{~g} \mathrm{~mol}^{-1}} \\ \therefore \quad & \frac{301.1}{149} \quad \therefore \mathrm{n}=2.02 \approx 2 \end{aligned}$ Thus, it is a bcc crystal structure.

Asked in: MHT CET 2024 (15 May Shift 2)

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