lab 6 franck hertz

Physics 318-L

Laboratory Report

Measurement of the Critical Potential of He Using a Modified Franck-Hertz Apparatus

Laboratory No.3

Written by: Eric Krage Lab Section 01

Lab Partners: Sarah McMahon, Haaken Phelps, Alan Halstrom Date Performed: 1/22/12

Instructor: Dr. McTaggart

Abstract:

The determination of planks constant using the PASCO h/e apparatus the value of planks constant was found to be 6.821*10-34 compared with the theoretical 6.626*10-34 yields a 2.9% error. This value is found by doing a linear fit to stopping potential vs. frequency with an R2=0.989; plotting the 95% confidence intervals it includes the theoretical value of Plank’s constant which is also included in the upper and lower prediction limits. This method of measuring planks constant can be concluded as accurate.

Apparatus

OriginPro 8 graphing utility Keithley Model 617 Programmable Electrometer SDSU:D13359 1.5 V dry cell battery Fluke 27/FM Multi-meter Heathkit 5.0 V DC regulated supply (model IP-27) Serial No. 13527 Helium Critical Potentials Tube and Universal Stand Computer – Gateway 2000 Labview (Franck-Hertz.vi)

Background

In 1914, James Franck and Gustav Hertz performed a pivotal experiment in the modern physics era. Their experiment verified the quantum theory, in which atoms have discrete energy levels. In short, the two used a beam of electrons accelerated through mercury vapor. It was seen that the kinetic energy of the electrons reached 4.9eV the mercury vapor emitted a spectrum line at 254nm. This discovery laid the initial building blocks for the investigation of the atomic structure of multiple elements, which, were the first steps in understanding the current understanding of the orbitals in an electron.

Figure 1 Franck Hertz Left and Gustav Hertz Right.

Prior to 1914 Bohr had proposed this model of the atom, where the electron moved in a circular path around the nucleus with angular momentum in integer multiples of h(bar). The Franck-Hertz experiment offered the first evidence of atomic quantization that did not involve emission lines. They excited the atoms with incident electrons, and discovered only certain energies were accepted by the atoms. The experiment directly demonstrated atoms accept energy in discrete packets of energies rather than just emitting it.

Procedure

The initial step was finding and verifying the working order of all of the equipment. The first goal was to examine the equipment we had to be able to determine the experimental setup to use. Through identification of all of the parts we had obtained we decided we would use experiment setup (tube type B). A schematic diagram of the experimental setup for the tube type B is figure 3 included as an appendix in the laboratory manual.

The second step was interfacing the device with the Vernier instrument and labview. The Franck-Hertz.vi was used to try to initialize the Keithley 617 to the take control and automatically vary the potential voltage. The updated software made it not possible in our allotted time to use this computer.Switching to the older computer and using the same LabView Franck-Hertz.vi we were able to initialize the Keithley 617 with the computer.

Using the Keithley 617 and setting the potential voltage we set the current source not to exceed the 1.4A suggested in the laboratory manual. For measurements, the potential difference between the anode and the loop was set to 1.5V. If the filament current was varied from 1.0, 1.2, and 1.4Amps; the anode current with the accelerating voltage VA=0 was 30-50pA. The first peak occurred at VA = 23s = 19.8 = 20.5V in the case of If=1.0A, was clearly observed, which lead to the conclusion that the conditions achieved were desirable. Key step is to allow the circuitry to arrive at steady state before taking data otherwise transient circuit behavior will be observable. Data was taken for the range from 15-30V in steps of 0.1V the results of the data acquisition will be found in the data section.

Note to open the files created by the Franck-Hertz.vi you will save the data in a file in a known location the file type will be saved as a .dat file. Using Microsoft Excel click the open files and select the extension .all files(**) this will allow you to see the .dat files you have created. Now select the file you want to open and when asked to choose the file type that best describes your file choose select delimited and click next. In the delimiters section have the tab option selected and space. This will open your data in a directly usable form and able to be used from there. When transferring to Origin8proPlus use the copy exact values otherwise Excel will limit the decimal places carried.

Data

Figure 1: If = 1.4Amps

Table 1:

Theoretical (eV) Experimental (eV) Error (%) Corrected (eV) Error (%)

19.8 21.2 7.2 20.7 4.55

20.9 21.4 2.4 20.9 0

22.9 22.9 0 22.4 2.18

24.6 24.1 2.0 24.6 0

Correction Factor 24.6-24.1=0.5

Figure 2: If = 1.2 Amps

Table 2


19.8 20.8 5.1 19.9 0.5

20.9 21.2 1.4 20.3 2.87

22.9 21.5 6.11 22.7 0.87

24.6 23.7 3.66 24.6 0


Figure 3: If = 1.0 Amps

Table 3


19.8 20.5 3.53 20.2 2.02

20.9 21.2 1.44 20.9 0

22.9 23.4 2.18 23.1 0.87

24.6 24.3 1.22 24.6 0


Result Analysis

Figure 4: The energy level diagram for Helium showing the singlet and triplet states.

Table 4: Ionization Potential/Energy levels

Energy (eV) Ionization

24.6 Potential

23.08 31p

23.00 33p

22.91 31s

22.71 33s

21.21 21p

20.96 23p

20.61 21s

19.80 23s

0.0 11s

The results were graphed as a plot of Ic vs. VA which shows 4 maxima in Figure 1, 2, and 3. The peaks in collector current are related to the He atoms absorbing energy form the electrons via excitation or ionization. The lower energy electrons are then drawn to the collector loop. The He peaks are not related to a single excitation energy but multiple. The excitation energy can be determined from figure 4 the energy level diagram; not all of these values were observed. The absorption of the energy when compare with the standard values are displayed in Table 1, 2, and 3. The correction factor was found from the equation below.

24.6 eV−Highes Peak=Correction factor

There were three data sets taken for each value of If and they were averaged and used as the data for the final data set. The accepted values for the principal energy levels of the helium are represented next to the calculated in the tables. The potential should be the result of exciting a ground-state electron to some higher energy orbital. This gave rise to the correction or shifting factor which represents the contact potentials. When compared with the laboratory manual the data seemed to have the overall shape when compared with the standard, therefore, the data was said to be well correlated to the accepted excitations.

Conclusion

Comparing this laboratory procedure to the experiment by Franck and Hertz was comparable and equally as rewarding in knowledge. From the graphs we concluded that certain only specific energies are absorbed and given off. These excitation potentials in He, occur, due to the transition of ground-state electrons to that of higher principal quantum numbers until the atom becomes fully ionized. The overall goal was achieved to more fully understand the quantization of energy levels.

References

1. An introduction to Error Analysis, John R. Taylor. 2nd Edition

Appendix.

lab 6 franck hertz

Documents