USAAAO — 2025 First Round

Which of the following statements are correct regarding spectral broadening? P: In the limit of zero temperature, spectral lines have infinitesimally narrow linewidth. Q: Consider two hypothetical spectral lines: line I has central frequency f₀ and full width at half maximum (FWHM) w ≪ f₀, with only homogeneous broadening; line II has identical central frequency and FWHM but only has inhomogeneous broadening. Let P(f)Δf denote the probability of measuring frequency f for each line within some bandwidth Δf ≪ w. Then, P_I(2f₀)Δf < P_II(2f₀)Δf. R: The same spectral line of two ideal gases, one with temperature T and the other with temperature 2T, are probed. The gases are otherwise identical. The linewidth of the hotter gas under thermal Doppler broadening is twice that of the cooler gas.