Calculate the volume of simple cubic unit cell if the radius of particle in it is 400 pm .

Calculate the volume of simple cubic unit cell if the radius of particle in it is 400 pm .
  1. $6.36 \times 10^{-22} \mathrm{~cm}^3$
  2. $5.12 \times 10^{-22} \mathrm{~cm}^3$
  3. $5.84 \times 10^{-22} \mathrm{~cm}^3$
  4. $6.60 \times 10^{-22} \mathrm{~cm}^3$

Solution

$\begin{aligned} & \quad r=\frac{a}{2} \\ & \therefore \quad \begin{aligned} a & =2 r=2 \times 400 \mathrm{pm}=800 \mathrm{pm} \\ \text { Volume }=\mathrm{a}^3 & =(800 \mathrm{pm})^3 \\ & =5.12 \times 10^{-22} \mathrm{~cm}^3\end{aligned} \\ & \quad\end{aligned}$

Asked in: MHT CET 2024 (10 May Shift 2)

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