The absorption cross section on the ordinate of the ozone absorption spectrum at the beginning of this chapter is defined by the relation

where n is the number of absorbing molecules per cubic centimeter, is the absorption cross section (cm²), and b is the pathlength (cm). The total ozone in the atmosphere is approximately 8×10¹⁸ molecules above each square centimeter of Earth's surface (from the surface up to the top of the atmosphere). If this were compressed into a 1-cm-thick layer, the concentration would be 8×10¹⁸ molecules/cm³.

(a) Using the ozone spectrum at the beginning of the chapter, estimate the transmittance and absorbance of this 1-cm³ sample at 325 and 300 nm.
(b) Sunburns are caused by radiation in the 295- to 310-nm region. At the center of this region, the transmittance of atmospheric ozone is 0.14. Calculate the absorption cross section for T= 0.14, n = 8×10¹⁸ molecules/cm³, and b = 1 cm. By what percentage does the transmittance increase if the ozone concentration decreases by 1% to 7.92×10¹⁸ molecules/cm³?
(c) Atmospheric O₃ is measured in Dobson units (1 unit = 2.69×10¹⁶ molecules O3 above each cm² of Earth's surface). (Dobson unit thickness [in hundredths of a millimeter] that the O₃ column would occupy if it were compressed to 1 atm at 0 C.) The graph shows variations in O₃ concentration as a function of latitude and season. Using an absorption cross section of 2.5×10¹⁹ cm², calculate the transmittance in the winter and in the summer at 30° -50° N latitude, at which O₃ varies from 290 to 350 Dobson units. By what percentage is the ultraviolet transmittance greater in winter than in summer?

30 N-50 N 10 N-30 N 10 N-10 S d 260 230 L1989 L1990 1991 1992 L1993 Year