Re: [Phys-L] colors when electrons scatter from a gas

[John Denker <jsd@av8n.com>]

On 3/10/22 8:15 AM, Carl Mungan via Phys-l wrote:

> Someone asked me what determines the colors when an electron beam
> scatters from gas atoms (an example would be the bluish light seen as
> the beam track in the introductory e/m experiment)?
>
> The question specifically is why one sees only the 492 nm line (see
> https://physics.stackexchange.com/questions/79441/which-cyan-colored-line-is-produced-in-the-thomson-e-m-apparatus
> <https://physics.stackexchange.com/questions/79441/which-cyan-colored-line-is-produced-in-the-thomson-e-m-apparatus>)
> and not the full visible spectrum of helium that one sees from a
> helium discharge tube (done in a different introductory lab
> experiment)?
>
> We suppose it has something to do with a trade-off involving gas
> density, state lifetimes, and the electron beam current.

I think it's simpler than that, if I understand the setup:

As pointed out in that stackexchange discussion, the electron
energy in that experiment is huge compared to the relevant atomic
levels. So I would imagine that hundreds of states are involved,
and thousands of transitions, not just one pure spectral line.

The eye is only sensitive to a tiny subset of the emitted light.
And the glass will block some of the hottest UV.

It's gonna be a big pachinko machine, as high-lying states
cascade down to lower states, emitting light at each transition.

Commonly a given state can decay in multiple ways, to maybe a
slightly-lower state or a much-lower state. The bluer transition
will be more intense, for reasons based in the Maxwell equations:
the higher frequency corresponds to more /acceleration/, and
accelerated charges do all the radiating. You can make a fancier
argument using Fermi's golden rule, but it comes down to the same
thing.

Many of the super-high frequency transitions will be disallowed
by selection rules. Conservation of angular momentum and all that.

Light that is a broad mixture with a bias toward blue could be
described as cyan ... or, better, a washed-out /pastel/ cyan.

The eye is more sensitive to green than blue, and green much
more than red, so that also contributes.

You can check all this using a spectrophotometer.