= Chapman ozone equilibrium
{c}
<Chapman ozone equilibrium> balances production and destruction of <atomic oxygen> and <ozone> in a minimal oxygen-only <atmospheric photochemistry> model. Write square brackets for <number densities>. Define <photolysis rate coefficients> $J_1,J_3$ and collisional <rate constants> $K_2,K_4$ by
$$
\begin{aligned}
\mathrm O_2+h\nu&\longrightarrow2\mathrm O &&(J_1),\\
\mathrm O+\mathrm O_2+\mathrm M&\longrightarrow\mathrm O_3+\mathrm M &&(K_2),\\
\mathrm O_3+h\nu&\longrightarrow\mathrm O_2+\mathrm O &&(J_3),\\
\mathrm O+\mathrm O_3&\longrightarrow2\mathrm O_2 &&(K_4).
\end{aligned}
$$
The collision partner $\mathrm M$ removes excess formation <energy> without being consumed. The third-body requirement reflects <conservation of energy> and <momentum conservation> during ozone formation.<A Theory of Upper-Atmospheric Ozone by Sydney Chapman>[Sections 5–9: dissociation, recombination and third-body stabilization]{ref}
Adding the <reaction rate> equations for <atomic oxygen> and <ozone> cancels their rapid interconversion. A local <steady state> gives
$$
[\mathrm O][\mathrm O_3]=\frac{J_1[\mathrm O_2]}{K_4}.
$$
If ozone loss is predominantly photolytic, $J_3\gg K_4[\mathrm O]$, its separate balance is
$$
K_2[\mathrm O][\mathrm O_2][\mathrm M]\simeq J_3[\mathrm O_3].
$$
Combining the two balances yields
$$
[\mathrm O_3]\simeq[\mathrm O_2]\sqrt{\frac{K_2J_1[\mathrm M]}{K_4J_3}}.
$$
The two factors of two in oxygen-atom production and destruction cancel in the first balance. This is a sunlit local <steady state>, with specified <temperature>, radiation and background <number densities>; transport and additional catalytic chemistry need not obey this four-reaction estimate.
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