Electron Beam does not appear to be continous (CRT Experiment) https://www.youtube.com/watch?v=2xKZRpAsWL8
Why do you see patches of purple in the tube? Shouldn't there be continous lines of colour?
As far as I know, you see the rays because some of the electrons knock the electrons out of the gas contained in the tube. When the excited gas atom de-excites, it emits a photon which indirectly shows the path of the cathod rays. The gas spreads out throughout the tube and hence will get excited all along the path of the electron beam.
From the above explaination, you should see the purple as something continous rather than patches of purple. 
Why do purple patches appear?
 A: I guess you're talking about this part of the video:

It looks like the Franck-Hertz effect, due to the fact that the first (allowed) excited state of the atoms in the residual gas has a quantized energy.  The electrons are continuously accelerated by the electric field in the chamber as they move from the cathode to the anode.  Only when their energies become larger than the threshold for the atomic excitation do the electrons cause atomic transitions and emit light.
Wikipedia has this very similar image from a Franck-Hertz experiment in neon:

The emission regions in your video have a relatively complicated shape: there's a much longer gap near the cathode than between the emission regions, and there's initially a diffuse background throughout the tube which disappears shortly before the frame I captured.  The cause of this is not yet obvious to me: it could be something fundamental and interesting, or it could be an artifact of non-uniform electric fields in the tube, which is long an narrow and surrounded by dangly HV wires.
