 Solution

The lost ozone-column photolysis shielding is $\Delta N=20(2.69\times 10^{16})=5.38\times 10^{17}\mathrm{molecules}\mathrm{c}{\mathrm{m}}^{-2}$, so its optical-depth decrement is $\sigma \Delta N=0.0538$. Under the stipulated effective-cross-section Beer-Lambert model, the transmitted photodissociation flux increases by $\exp (0.0538)$.

The short-lived oxygen singlet D atom satisfies $[\mathrm{O}({}^{1}D)]\simeq J_{{\mathrm{O}}_3}[{\mathrm{O}}_3]/(k_q[M])$ when quenching dominates. At fixed local ozone, water and air density, hydroxyl radical production is proportional to $J_{{\mathrm{O}}_3}$. ConsequentlyA linear optical-depth approximation would give $5.38\%$. A realistic calculation integrates the wavelength-dependent absorption cross section, quantum yield and actinic flux; clouds and multiple scattering modify the simple transmitted-beam model.

Ozone change can also alter the radiative temperature structure, water vapor and circulation, thereby changing the water reaction channel and the supply of ozone/precursors to the troposphere. If the held-fixed tropospheric ozone assumption is relaxed, altered ozone itself changes the photochemical source of oxygen singlet D atom. These are additional feedbacks, distinct from the isolated UV-transmission calculation above.