The absorption cross section on the ordinate of the ozone absorption spectrum at the

Chapter 17, Problem 17-14

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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 Earths 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 . Transmittance (T) enb (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 Earths 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?