Question

All objects at a given temperature emit thermal radiation, which results in a continuous spectrum. Given that the discharge tubes were at some temperature (~50 C), use Wien's displacement law to argue why you dont see the continuous spectrum when looking at the gas with the spectrometer. Please use wein's law

Answer 1

The light from a discharge tube is a totally different kind of radiation process than thermal radiation. In a diffuse gas, the atoms are so far apart, that (to an approximation) the only significant effect is the electrons in individual atoms transitioning between levels in their atoms. Because the electron levels are quantized, only certain frequencies of light are emitted when the electrons transition between levels. The frequency of the emitted light corresponds to the energy lost by the electron in going down an energy level according to E = hf. A similar process happens in lasers and is why laser light has approximately a single frequency. A spectrum from a diffuse gas is called a line spectrum.

In contrast to diffuse gases, dense gases, liquids and solids have their atoms so close that they are constantly knocking into each other, absorbing each others' radiation and re-emitting it at a different frequency because the atomic collisions take some energy away. All of this thermal motion of the atoms causes the original line spectrum of the individual atoms to be smeared out into a broad, thermal spectrum.

The perfect blackbody thermal spectrum and the perfect line spectrum with perfectly narrow lines are idealizations. In reality, real spectra lie somewhere in between the two. The more dense and the higher the temperature, the more the spectrum looks like a blackbody curve and less like a line spectrum. Even laser light does not have a perfectly thin spectrum with exactly one frequency, but experience thermal broadening.