, 1 min, 157 words
Tags: physics
The way that sunscreen works is using a certain molecule, oxybenzone, which can absorb UV photons and reemit lower-frequency photons. Based on the fact that it absorbs photons with around 100-nm wavelengths, we know that the energy difference between its ground state and its first excited state is exactly the energy carried by such a photon, which is simply $\frac{hc}{\lambda}$. So we can actually calculate the probability that any given oxybenzone molecule is in an excited state at beach-temperature (independent of the incoming UV, which is greatly reduced by the atmosphere). It turns out that only about one in 10^200 oxybenzone molecules is in its excited state because of the ambient temperature (around 300K). That's a seriously small fraction, and speaks to the effectiveness of sunscreen.
Another convenient thing about oxybenzone is that it is soluble in most organic solvents (nonpolar) and less so in water, so it's fairly water-resistant.