If ionic radius of Cs+ and Cl- are 1.69 Ao and 1.81 Ao respectively, the edge length of unit cell is_ in same units(Round off to nearest integer)

# If ionic radius of Cs+ and Cl- are 1.69 $\stackrel{\mathrm{o}}{\mathrm{A}}$ and 1.81 $\stackrel{\mathrm{o}}{\mathrm{A}}$ respectively, the edge length of unit cell is_ in same units(Round off to nearest integer)

1. A
2. B
3. C
4. D

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### Solution:

$\begin{array}{l}2\left({\mathrm{r}}^{+}+{\mathrm{r}}^{-}\right)=\sqrt{3}\text{\hspace{0.17em}}\mathrm{a}\\ 2\left(1.69+1.81\right)=\sqrt{3}\text{\hspace{0.17em}}\mathrm{a}\\ 2×3.5=\sqrt{3}\text{\hspace{0.17em}}\mathrm{a}\text{\hspace{0.17em}}⇒7=\sqrt{3}\text{\hspace{0.17em}}\mathrm{a}\\ \mathrm{a}=\frac{7}{\sqrt{3}}=4.04\text{\hspace{0.17em}}\stackrel{\mathrm{o}}{\mathrm{A}}\end{array}$

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