If an average \(\mathrm{O}_{3}\), molecule "lives" only \(100-200\) seconds in the stratosphere before undergoing dissociation, how can \(\mathrm{O}_{3}\) offer any protection from ultraviolet radiation?

First, it's important to grasp the role that ozone molecules play in the stratosphere. Ozone absorbs harmful ultraviolet (UV) radiation from the sun, preventing it from reaching the Earth's surface. UV radiation is divided into three types: UVA, UVB, and UVC. Ozone primarily absorbs UVB and UVC radiation, which can harm living organisms and cause skin cancer in humans.

Ozone is formed through a series of chemical reactions involving oxygen molecules (O2) and individual oxygen atoms (O): 1. Oxygen molecules (O2) absorb UV radiation, which dissociates them into two oxygen atoms (O): \[ O_2 + \text{UV} \rightarrow 2O \] 2. The free oxygen atoms (O) then react with other oxygen molecules (O2) to form ozone (O3): \[ O + O_2 \rightarrow O_3 \] 3. Ozone molecules (O3) can also absorb UV radiation, causing them to dissociate back into an oxygen molecule (O2) and an oxygen atom (O): \[ O_3 + \text{UV} \rightarrow O_2 + O \] The balance between the formation and dissociation of ozone creates a steady-state ozone concentration in the stratosphere.

Ozone's short lifespan in the stratosphere indicates that ozone molecules are constantly undergoing formation and dissociation processes. When ozone absorbs UV radiation, it dissociates to form oxygen molecules and atoms, which in turn participate in further ozone formation processes. As a result, despite the short lifespan of individual ozone molecules, there is always a steady-state concentration of ozone in the stratosphere that effectively absorbs and blocks harmful UV radiation from reaching the Earth's surface. In conclusion, the constant formation and dissociation of ozone in the stratosphere ensure that there is always a sufficient concentration of ozone to protect the Earth from harmful ultraviolet radiation, despite the short lifespan of individual molecules.