Nitrogen gas in a heated cell is illuminated by an argon-ion laser at ( )

PHYSICS · Subjective · Fermi University Physics · Atomic, Molecular & Optical Physics · Molecular structure and spectra · Molecular structure and spectra

Deriving the Spectrum, Ch Electronic spectra of diatomic molecules

Problem

Nitrogen gas in a heated cell is illuminated by an argon-ion laser at 488 nm488\,\mathrm{nm} (ν~0=20 491.8 cm−1\tilde\nu_0 = 20\,491.8\,\mathrm{cm^{-1}}). The N2\mathrm{N_2} vibrational Raman shift is ν~v=2331 cm−1\tilde\nu_v = 2331\,\mathrm{cm^{-1}}. The measured ratio of the anti-Stokes to the Stokes vibrational line intensities is Ias/Is=3.0×10−3I_{\rm as}/I_{\rm s} = 3.0\times10^{-3}. Using IasIs=(ν~0+ν~vν~0−ν~v)4e−hcν~v/kBT,\frac{I_{\rm as}}{I_{\rm s}} = \left(\frac{\tilde\nu_0 + \tilde\nu_v}{\tilde\nu_0 - \tilde\nu_v}\right)^4 e^{-hc\tilde\nu_v/k_{\rm B}T}, find the gas temperature TT. Take hc/kB=1.4388 cm Khc/k_{\rm B} = 1.4388\,\mathrm{cm\,K}.

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