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Helium Excitation

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Abstract

In this experiment the excitation of the He atoms to discrete energy levels is observed and analyzed. The manner in which the excitation occurs is by bombarding the He atoms with electrons that originate from a tungsten cathode. Excitation only occurs when the mean energy of the colliding electrons is sufficient enough to sustain inelastic collisions with the He atoms. The inelastic collisions will define the different energy levels that the He atoms possess and these will be analyzed. The method in which the energy levels will be studied is through the form of graphs which contain peaks that correspond to a certain current and potential.

Introduction

The excitation of Helium to its discrete/higher energy levels requires equipment of relatively high sensitivity. The main instrument used in the excitation of He atoms in this experiment is that of a Critical Potentials Tube. The helium is contained in the tube at low pressure and it is bombarded with electrons. If the electrons have a certain “critical” energy they will undergo inelastic collisions with the He atoms. The electrons that have collided with the atoms will have their energy depleted from them and they are further attracted to the slightly positive collector ring which produces a certain current relative to the amount of electrons that are collected. A relation with the amount of electrons that induce a current within the collector ring and the discrete/higher energy states of Helium can be determined by the form of a current vs. potential plot. The peaks of the graph would correspond to the amount of energy required for excitation and the energy required for the ionization.

Theory

This experiment takes advantage of the Critical Potentials Tube. This apparatus consists of a blub that contains Helium at a low pressure. Now, the inside of the blub is laminated with a conducting layer (stannous chloride) which is connected to an anode. The blub also has a collector ring in order to read the current. Further, the filament (tungsten cathode) is where the electrons originate hence a voltage is applied for this to occur. The electrons leaving the tungsten cathode are further accelerated by the anode which is connected to the inside layer of the bulb. The purpose of this is so that electrons that make contact with the inside layer of the bulb will go back to the anode from which it was accelerated from through the conducting layer. These electrons that go back to the anode are attracted to the collector ring which has a slight positive charge. This is where there will be a change in current because of the near-zero energy electrons that have undergone inelastic collisions with the He atom. Further, this change in current can be graphed using an x-y plotter which has current input connections. Now, the voltage that corresponds to the peaks in the graph is the necessary or critical energy that is required to excite the He atoms to higher energy states. As already mentioned this relation is seen in the current vs. potential plots. The more electrons that are attracted to the collector ring is related to the energy required to excite the Helium. Once these observations are noted these peaks can be compared to the principal energy levels of helium and its critical potential in order to verify the theory.

Procedure

The procedure that was followed was outlined in the write-up provided for Experiment #18.

Discussion

In the first part of the experiment the filament voltage was varied. The voltages of 1.8V, 2.1V and 2.3V were graphed using the x-y plotter. There is a lot of similarity between the graphs especially between the graph of 1.8V and 2.1V. These two graphs seem to be almost identical with the exception of a gap between them when placed together. Other than the fact for the offset these graphs have their peaks in relatively the same areas. The significant difference between the 1.8V and 2.1V graph is that there is an increase in current for the 2.1V graph. The 2.3V graph is quite similar is terms of its shape in comparison to the other two graphs but it is quite evident that it has a higher current. It is also evident that once ionization begins the slope of the graph at that point is much steeper than that of the 1.8V and 2.1V graph. Even though it looks similar to the first two graphs the peaks in the graph are much larger. The reason why the graph has a higher current could be accounted for the fact that there are more inelastic collisions occurring in the blub between the electrons and helium atoms so that means more near-zero energy electrons are being attracted to the slightly positive collector ring. Moreover, there were a number of precautions taken in order to minimize the presence of external electric fields. While the experiment was being conducted the door to the room was shut, all electrical devices that were on both experimenters were moved away from the equipment. Also, while the apparatus was running both experimenters tried to minimize their movements to the best of their ability so that they did not interfere with the experiment and to further reduce any external fields the lights in the room were also turned off.

The correction value that was determined from the first peak was 2.33V. It can be seen that the calculated potentials are in close proximity to the reference values that were given. Since the first peak was used to determine the correction value for the rest of the energy levels the first calculated potential is equivalent to the reference value (Reference – Calculated = Correction Value). The first two energy levels were calculated to be 19.80V ±0.37V and 20.57V ±0.41V. These two values are very close to the reference values as with the third energy level. The calculated potential for the third energy level is 22.83V ±0.45V which differs from the accepted value by 0.31%. Further, the calculated potentials for the fourth and fifth energy levels were determined by referring to the 3¹D and 3³D shells of the Helium atom. Moreover, the results of the calculation are shown in the table below:

Energy Levels

Calculated Potential

Uncertainty

Reference Value

Percent Difference

1

19.80V

±0.37V

19.8V

0.0%

2

20.57V

±0.41V

20.9V

1.57%

3

22.83V

±0.45V

22.9V

0.31%

4

23.09V

±0.46V

23.21V

0.52%

5

23.78V

±0.47V

23.45V

1.41%

The ionization of helium was determined to be 24.82V ± 0.48V. Further, in order to determine the ionization potential the current input connections of the x-y recorder were reversed and the polarity of the battery was switched. What this does is that once the helium has been ionized the electrons that are freed from it are attracted to the slightly positively charged collector ring while the input electrons which have in elastically collided with the helium atom are attracted to the ground of the tube. At this point the process of determining the energy required to ionize helium is the same as determining the energy required to excite it. The relation between the amounts of electrons that are attracted to the collector ring to the input beam is used to determine the energy required to ionize helium. This can be seen on a graph when there is a rapid increase of current. Moreover, under closer observation of the ionization potential graph it was noticed that there were two points where the current increased before the rapid increase stage (beginning of ionization). This can be accounted for the fact that there are some atoms (a small percentage) that have already started the process of ionizing before the rest. The only explanation for this is that the external electric fields that are present in the room allow for the ionization of these few atoms.

Conclusion

In conclusion, this experiment has proved the validity of the theory. The measured/calculated values were all in close proximity to the accepted values predicted by the theory.

Sample Calculations

Sample Calculation of error in Excitation Potential

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Sample Calculation for determination of Correction Voltage
Accepted Value: 19.80 V
Calculated Value: 17.47 V
Correction Voltage: 19.80 V – 17.47 V = 2.33 V

References

“E18 Helium Excitation”, University of Waterloo, Physics 360A, 2008.