Please answer all parts and be legible. Thank you!

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Please answer all parts and be legible. Thank you!

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Absorption of Radiation by Atoms and Molecules, part a O points possible (ungraded) Electromagnetic radiation (photons) can be absorbed by atoms and molecules if the energy of the incoming photon is equal to the energy associated with transitions in energy levels of the atoms or molecules. The energy and wavelength of a photon are related by E ho X where h is the Planck constant, , is the wavelength of the photon, and c is the speed of light. There is some bandwidth in the allowed energies of the absorbed photons due to a variety of factors, including a fundamental uncertainty in the energy of the photon as well as effects due to temperature and pressure. In the figure below, the power per area of the solar radiation is plotted vs. wavelength for a blackbody at 5780 K (black curve), the radiation at the top of the atmosphere, and the radiation at sea level [1]. The absorption bands due to ozone 03 (which completely absorbs ultraviolet radiation), water vapor H20, and carbon dioxide CO2 are shown. 2. 5780 K blackbody sunlight at top of atmosphere (AM 0) radiation at sea level (AM 1.5) 1.5 spectral irradiance [W/m² nm) 1. H2O 0.5 03 H2O H20 CO2 02 H2O 250 500 750 1000 1250 1500 1750 2000 2250 2500 wavelength [nm] [1] Figure courtesy of R. Jaffe, from Jaffe and Taylor, Physics of Energy, p.440. Shown in figure below is the power spectrum of outgoing infrared radiation. In bands in which there is substantial IR absorption, the outgoing radiation is emitted from higher up in the atmosphere hence at lower temperatures. The blackbody emission spectrum at various temperatures are shown in the dashed red lines [2].
wavenumber [cm-?] 1 000 1 500 500 H2O 03 CO2 H20 100 CH4 N20 radiance [mW/(m? sr cm)] 280 Kaina 260 K 50 240K 220 K awy 7 8 9 10 15 20 wavelength [um] [2] Figure courtesy of R. Jaffe, from Jaffe and Taylor, Physics of Energy, p.694. (Part a) Carbon dioxide CO2 has two vibration modes that can absorb photon energies: (i) E1 = 0.291 eV and (ii) E2 = 0.083 eV. What are the associated wavelengths of the absorbed photon? Recall that h = 6.626 x 10–34 Js, c=299792458 m.s-1, and 1 eV = 1.602 x 10-19 J. Check your numeric answers below. , 11 = .004 m X .004 12 = 0.00002 m x 0.00002
Absorption of Radiation by Atoms and Molecules, part b 0 points possible (ungraded) = (Part b) Assume the earth is a blackbody at T = 300 K. Use the Wien Displacement Law in the form \max = , where the constant of proportionality is called Wien's displacement constant and is equal to 2.90 x 10-m-K, to find the wavelength 3 Imax that corresponds to the maximum of the earth emission spectrum. Check your numeric answer below. Imax = .0097*10^(-3) m .0097 . 10-3 Submit Absorption of Radiation by Atoms and Molecules, part c 0 points possible (ungraded) (Part c) In the absorption spectra shown in the figure below [3], estimate the transition energies for water vapor associated with two absorption bands in the wavelength range 2 x 10-6 m << 8 x 10-6 m. Check your numeric answers below. El corresponds to the lower-wavelength absorption band, and E2 the higher-wavelength absorption band. E = .586 eV X .586 E2 = .15 eV X .15
3 10 30 70 0.7 1 100 75 50 25 total absorption major components ou un H20 CO2 O2,03 CH4 N20 30 0.7 1 3 70 10 wavelength [um] [3] Figure courtesy of R. Jaffe, from Jaffe and Taylor, Physics of Energy, p.688.