The question of how the line spectrum of atoms is transformed into the continuous spectrum of thermal radiation of a gas by repeated absorption and emission of photons is addressed. We consider a simple model of a hydrogen-like gas in thermal equilibrium where only the Lyman-α transition is allowed and calculate the spectra for increasing thickness of the gas. The transition from line spectra for optically thin samples to the spectra of thermal radiation for optically thick samples is demonstrated. We estimate the emissivities for hot gases and study the line width of spectral lines due to self-absorption processes.
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