You are strolling along a tropical beach observing Canadian tourists as they sunbathe (for the sole purpose of scientific enlightenment, of course). You pay particular attention to the rate at which observable erythema (sunburn) occurs on light-skinned individuals. You make the following observations (on skin surfaces that are facing directly toward the sun):

Observation 1: Around noon, the sun is directly overhead. It takes 12.0 minutes for noticeable reddening to appear on a typical sunbather.

Observation 2: Later, when the sun is about 45° above the horizon, it takes 60.0 minutes for the same degree of sunburn to occur. [Assume that the change in the sun's elevation during the observation can be neglected.]

Simplifying assumptions: Assume that all UV-B radiation responsible for sunburn is concentrated at a single wavelength, l = 300 nm, and that ozone is the only atmospheric species that absorbs this wavelength. Treat the ozone layer as a layer of pure gas at STP with equivalent thickness 3.00 mm.

Assume that the degree of sunburn is directly proportional to the quantity of UV-B radiation (per unit area) incident upon the skin = (intensity) x (time of exposure).

(a) Calculate the value of the absorption coefficient aa, for λ = 300 nm in pure ozone.

(b) What is the absorbance of the atmosphere (fraction of incident radiation that is absorbed) for this wavelength, when the sun is directly overhead? What is the absorbance when the sun is 45° above the horizon?