Question
Ozone is a gas heavier than air. Why does ozone layer not settle down near the earth?

Answer

In stratosphere, the formation of $\mathrm{O}_3$ goes on continuously, but $\mathrm{O}_3$ is also decomposed by UV-radiation between 240 to 360nm.
$\text{O}_3+\text{h}\upsilon\xrightarrow{ \ \ \ (240-360\text{nm}) \ \ \ }\text{O}_2+\text{O}$
The O -atom reacts with second $\mathrm{O}_3$ molecule. $\mathrm{O}_3+\mathrm{O} \rightarrow 2 \mathrm{O}_2$ Net reaction $2 \mathrm{O}_3 \rightarrow 3 \mathrm{O}_2$ Thus, the reactions form a delicate balance in which the rate of $\mathrm{O}_3$ decomposition matches the rate of $\mathrm{O}_3$ formation, i.e., a dynamic equilibrium exists and maintains a constant concentration of $\mathrm{O}_3$.

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