According to QED, the energy levels of an electron bound to atom are quantized and require specific amounts of energy to excite valence electrons to a higher energy state. If that energy is not provided the transition to a higher energy level will not occur. When the electrons have more energy than required, an inelastic collision takes place, wherein the free electron deposits the required atomic energy and is then left with the excess energy not required for atomic transition. As the electron is slowed it can then be collected by the ring collector. As the energy of the electrons approaches the energy levels of the neon, the electrons will be robbed of most of their energy, and the collected current will peak sharply. These peaks will signify the value of the energy levels in the neon gas.
Materials and methods
Hertz Critical Potentials tube filled with neon
Picoamplifier and Alarmed Meter
2 HP Power Supplies
Fluke 111 true rms multimeter
The experiment is detailed very well in the lab manual under Excitation and Ionization of Neon. 
Figure 1: This is a schematic of the Hertz Critical Potentials tube. The filament is heated and electrons are released and accelerated by the cathode/anode. The energetic electrons collide with the inert neon gas and the resultant slowed electrons are captured by the wire ring collector.
Figure 2: Setup and connection of the apparatus. The filament is connected to voltage Vf which provides the current to boil electrons off of the tungsten hairpin filament. The anode and cathode are connected to voltage Va, the accelerating voltage which provides the electrons with kinetic energy. The wire ring collector is provided with voltage Vc, to collect the slowed electrons, through a picoamplifier and ultimately to a meter to provide a readout of the current.
After setting up the circuit in Figure 2, the heater was set to a voltage which provided a suitable current while the accelerating voltage was kept at zero. The ammeter connected to the picoamplifier was zeroed using a knob on the base of the amplifier. We then started to increase the accelerating voltage on the grid, all the while monitoring the current on the collector ring. Using small increments in the accelerating voltage, we can plot Va vs. Ic (collector current) to determine the peaks or energy levels of the neon.
The data that was collected can be found in my notebookPhysics307L F07:People/Gleicher/Notebook/071119
The following is a plot of the data with the polarity on the collector ring being reversed. The voltage on the filament is 2.00 V
The next plot shows the relation between Va and Ic when the polarity on the collector ring is positive with respect to ground. The voltage on the filament is 2.476 V.
Looking at the two graphs, peaks can be found at approximately 16.25, 16.75, 18.25, and 20.50 V.
The values for energy levels given in the manual are 16.7, 18.65, 19.75, and 20.10 V.
Our measured values for the energy levels are very close to the given values and the % error for those values are as follows:
The average of the errors is 1.47%
Possible sources of error include the sensitivity of the apparatus to motion around the tube and the requirement to zero the meter. If the meter is not properly zeroed, then the measurements can be slightly off.