Please answer all parts and be legible. Thank you!
Posted: Fri May 06, 2022 10:32 am
Please answer all parts and be legible. Thank you!
Absorption of Radiation by Atoms and Molecules, part a 0 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 hc E = X where h is the Planck constant, X 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 O3 (which completely absorbs ultraviolet radiation), water vapor H₂O, and carbon dioxide CO2 are shown. 5780 K blackbody sunlight at top of atmosphere (AM 0) radiation at sea level (AM 1.5) 1.5 1. H₂O 0.5 03 H₂O H₂O CO2 H₂O 0 250 500 750 1000 1250 1500 1750 2000 2250 2500 wavelength [nm] [1] Figure courtesy of R. Jaffe, from Jaffe and Taylor, Physics of Energy, p.440. spectral irradiance [W/m² nm]
Shown in the 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] 1500 1 000 500 CH4 03 H20 . N₂0 7 8 9 10 15 20 wavelength [um] [2] Figure courtesy of R. Jaffe, from Jaffe and Taylor, Physics of Energy, p.694. -34 (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 × 10- c=299792458 m-s¹, and 1 eV = 1.602 × 10-¹⁹ J. Check your numeric answers below. J.s, A₁ = m X₂ = m radiance [mW/(m² sr cm-¹)] 100 50 H₂O 280 K 260 K 240 K 220 K CO₂
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 Amax=, where the constant of proportionality is called Wien's displacement constant and is equal to 2.90 × 10-³ m.K, to find the wavelength Amax that corresponds to the maximum of the earth emission spectrum. Check your numeric answer below. Amax = m 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 < X < 8 × 10-6 m. Check your numeric answers below. E₁ corresponds to the lower-wavelength absorption band, and E2 the higher-wavelength absorption band. E₁ = eV E₂ = eV
0.7 1 100 75 50 percent major components 3 10 30 70 total absorption H₂O CO₂ 02,03 CH4 N₂O 0.7 1 3 30 10 wavelength [um] [3] Figure courtesy of R. Jaffe, from Jaffe and Taylor, Physics of Energy, p.688. 70
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Shown in the 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] 1500 1 000 500 CH4 03 H20 . N₂0 7 8 9 10 15 20 wavelength [um] [2] Figure courtesy of R. Jaffe, from Jaffe and Taylor, Physics of Energy, p.694. -34 (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 × 10- c=299792458 m-s¹, and 1 eV = 1.602 × 10-¹⁹ J. Check your numeric answers below. J.s, A₁ = m X₂ = m radiance [mW/(m² sr cm-¹)] 100 50 H₂O 280 K 260 K 240 K 220 K CO₂
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 Amax=, where the constant of proportionality is called Wien's displacement constant and is equal to 2.90 × 10-³ m.K, to find the wavelength Amax that corresponds to the maximum of the earth emission spectrum. Check your numeric answer below. Amax = m 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 < X < 8 × 10-6 m. Check your numeric answers below. E₁ corresponds to the lower-wavelength absorption band, and E2 the higher-wavelength absorption band. E₁ = eV E₂ = eV
0.7 1 100 75 50 percent major components 3 10 30 70 total absorption H₂O CO₂ 02,03 CH4 N₂O 0.7 1 3 30 10 wavelength [um] [3] Figure courtesy of R. Jaffe, from Jaffe and Taylor, Physics of Energy, p.688. 70