I am trying to know whether it would be possible to do an undergraduate laboratory experiment to measure absorption lines produced by a gas. The idea is to have a background source of light with a continuous spectrum (either sunlight or an incandescent light bulb), a spectrometer, and some gas in between. I thought helium would be best, because it's easy to obtain, seems safe, and the amount of spectral lines is small (but I'm open to suggestions).
I imagine the attenuation in the intensity would be related to the optical depth ($\tau$), which in turn would be related to the absorption cross section ($\sigma$) and number density ($n$) of the gas. That is, the intensity after absorption ($I$) would be related to that before absorption ($I_0$) as $$I(\lambda)=I_0(\lambda)e^{-\tau(\lambda)},$$ where $\tau$ is something like $$\tau(\lambda)=\int_0^L n(\mathbf x) \left<\sigma(\lambda)\right>\,\mathrm dx. $$
If the gas is uniformly distributed in a container, $\tau(\lambda)=n L \left<\sigma(\lambda)\right>$, where $L$ is the length along the line of sight.
If the gas can be taken as ideal, I can relate $n$ to $p$ (pressure) easily. This would allow me to estimate a pressure threshold $p_\mathrm{th}$ that would produce enough attenuation to be detectable. This could be done by imposing an optical depth threshold around the central position of an absorption line, or a threshold on the integrated optical depth around it. Either way, it would be something like $$p>p_\mathrm{th}\sim\frac{\tau_\mathrm{th} kT}{L\left<\sigma\right>.}$$
So, my question is either of the following:
- where could I find data for $\left<\sigma\right>$ to figure this out on my own?, or
- does anyone with expertise know if this is feasible at all?
