$(a)\;\large\frac{V_{c}}{V_{s}} \approx 10^{-3}\qquad(b)\;\large\frac{V_{c}}{V_{s}} \approx 10^{3}\qquad(c)\;\large\frac{V_{c}}{V_{s}} \approx 1\qquad(d)\;\large\frac{V_{c}}{V_{s}} \approx 10^{23}$

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Answer : $\large\frac{V_{c}}{V_{s}} \approx 10^{3}$

Explanation :

For a true solution , the diameter range is 1 to $\;10A^{0}\;$ , and for colloidal solution , diameter range is $\;10 - 1000 A^{0}\;$ .

Taking lower limits ,

$\large\frac{V_{c}}{V_{s}}=\large\frac{\large\frac{4}{3} \pi r_{c}^{3}}{\large\frac{4}{3} \pi r_{s}^{3}}=(\large\frac{r_{c}}{r_{s}})^{3}$

We know ,

$r_{c}=\large\frac{10}{2}=5A^{0}\qquad \; , r_{s}=\large\frac{1}{2}=0.5A^{0}$

Therefore , $\;\large\frac{V_{c}}{V_{s}}=(\large\frac{5}{0.5})^{3}=10^{3}$

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