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problemset7

# problemset7 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6.007 Applied Electromagnetics Spring 2011 Problem Set 7 Due Wednesday April 6, 2011 Problem 7.1, Atmospheric CO2 Measurement Working at the Mauna Loa Observatory in beautiful, sunny Hawaii, you perform infrared absorption spec- troscopy to measure the concentration of CO 2 in air samples from the upper atmosphere. In their own words— [. . . ] Air is slowly pumped through a small cylindrical cell with ﬂat windows on both ends. Infrared light is transmitted through one window, through the cell, through the second window, and is measured by a detector that is sensitive to infrared radiation. In the atmosphere carbon dioxide absorbs infrared radiation, contributing to warming of the earth surface. Also in the cell CO2 absorbs infrared light. More CO2 in the cell causes more absorption, leaving less light to hit the detector. We turn the detector signal, which is registered in volts, into a measure of the amount of CO2 in the cell through extensive and automated (always ongoing) calibration procedures. 1 In this problem, you will use the Lorentz oscillator model to predict the peak absorption of atmospheric CO 2 by estimating its plasma frequency ω p , resonance frequency ω 0 , and linewidth γ . 1. For a dilute gas (i.e., a medium with small susceptibility), show that, r i n = r r κ = . (1) 2 n 2. Use the most recent (mean) CO 2 concentration (300 ppm) measured at Mauna Loa and the Ideal Gas Law to determine the number of CO 2 molecules per unit volume m 3 . Assume temperature is 300 K. Estimate the plasma frequency of this sample. What is an approximate index of refraction for a sample of this gas? 3. Figure 1 shows the absorption spectrum of CO 2 (taken from Lecture 20). Most infrared CO 2 lasers Figure 1: Observed gas absorption spectrum in the upper-atmosphere. Image created by Robert A. Rohde / Global Warming Art. Used with permission. http://www.globalwarmingart.com/wiki/File:Atmospheric_Absorption_Bands_png .

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problemset7 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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