Carbon dioxide gas

PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Wave propagation and light in media · Wave propagation and light in media

Optics and Photonics, Ch Light as an electromagnetic wave in matter

Problem

Carbon dioxide gas, used in fire extinguishers, has a density ρ=1.83 kg m−3\rho = 1.83\ \mathrm{kg\,m^{-3}} at room temperature and atmospheric pressure, and a molar mass M=44.01 g mol−1M = 44.01\ \mathrm{g\,mol^{-1}}. Avogadro's constant is NA=6.022×1023 mol−1N_A = 6.022\times10^{23}\ \mathrm{mol^{-1}}. As for the air estimate in the text, model each CO2\mathrm{CO_2} molecule as one effective oscillating electron with a single ultraviolet resonance, guessed at λ0=150 nm\lambda_0 = 150\ \mathrm{nm} (close to the onset of carbon dioxide's strong ultraviolet absorption). ((a)) Find the number density N\mathcal{N} of CO2\mathrm{CO_2} molecules from its density and molar mass. ((b)) Use the dilute-gas Lorentz formula to estimate n−1n - 1 for visible light of vacuum wavelength 589 nm589\ \mathrm{nm}, checking first that ω≪ω0\omega \ll \omega_0. ((c)) The tabulated refractive index of carbon dioxide at this wavelength and these conditions is n−1=4.49×10−4n - 1 = 4.49\times10^{-4}. Compare your estimate with this value and comment briefly on the size of any discrepancy.

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