An element with simple cubic close structure has edge length of unit cell $3.86 Å$. What is the radius of…

An element with simple cubic close structure has edge length of unit cell $3.86 Å$. What is the radius of atom?
  1. $5.79 \times 10^{-8} \mathrm{~cm}$
  2. $1.93 \times 10^{-8} \mathrm{~cm}$
  3. $3.86 \times 10^{-8} \mathrm{~cm}$
  4. $2.43 \times 10^{-8} \mathrm{~cm}$

Solution

In simple cubic close structure $\begin{aligned} & \mathrm{a}=2 \mathrm{r} \\ & \mathrm{r}=\frac{\mathrm{a}}{2}=\frac{3.86}{2}=1.93 Å \\ & \mathrm{r}=1.93 \times 10^{-8} \mathrm{~cm} \\ & \left(1 \mathrm{~A}^{\circ}=10^{-10} \mathrm{~m}=10^{-8} \mathrm{~cm}\right) \end{aligned}$

Asked in: MHT CET 2021 (21 Sep Shift 1)

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