Franck Hertz calculation

Hi, I would like you to do the calculation for Franck Hertz experiment. I have attached all you need to finish the calculation and answer the questions in each part. you will see the steps in the file called “Franck Hertz handout” . Moreover, use excel sheets are in the file called attachments for each Mercury and Neon. I want you to organize it based on the file called “Data analysis Report”. Moreover, I want you to write me a summary a short paragraph and answer the questions called pre-labs exercises under the short paragraph. So, There are two major things I want you to finish:1- do the calculation and analysis based on what the handout file, and Data analysis Report are asking you for. you have to write them on world document what Data analysis Reportare asking you for.2- write me in a different file a short paragraph about this experiment, and do the pre-lab exercises. Good luck and thank you,
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PHYS341: Data Analysis Report
(Even Numbered Experiments)
1. Objective (5)
2. Equipment & Procedure (10)
(Brief and succinct; must contain important info needed for someone else to
conduct this experiment).
3. Data Presentation (25)
(Emphasis on organization, Quality of Graphs, Tables etc.)
4. Data Analysis & Results (40)
5. Error Analysis (10)
6. Conclusions (10)
Franck – Hertz Experiment – Electron Spectroscopy
Objectives
? To verify the quantization of atomic electron energy states of mercury and neon
atoms by observing the maxima and minima of an electron current passing
through the gas.
? To understand how ordinary and metastable atomic electron energy states affect
the transmission of electrons.
? To understand how temperature affects the number density of atoms in gases, the
mean free path of a transmission electron, and the kinetic energy of a transmission
electron.
? To gain a familiarity with GPIB interfacing.
? To gain more expertise in LabView programming
Background Reading
1. Melissinos, Experiments in Modern Physics, (Academic Press, Second Edition), The
Franck Hertz Experiment.
2. Serway, Moses, Moyer, Modern Physics, (Saunders Publishing Co.., 1997), Direct
Confirmation of Atomic Energy Levels, pp. 132.
3. Preston, Dietz, The Art of Experimental Physics, John Wiley and Sons, 1991, pp.
197.
Introduction
The Franck – Hertz experiment, first performed in 1914, verified that the atomic
electron energy states are quantized, by observing maxima and minima in transmission of
electrons (i.e. electrical current) through a vapor. The variation in the electrical current is
caused by inelastic scattering that excites the atomic electrons in the vapor atoms. James
Franck and Gustav Hertz performed this very same experiment 12 years before the
development of quantum mechanics, and it provided striking evidence that atomic energy
states are quantized. They were awarded the 1925 Nobel Prize in Physics for “Their
discovery of the laws governing the impact of an electron upon an atom.”
In this experiment, you will perform the Franck – Hertz experiment for two
elements; mercury and neon. A theoretical background of the experiment will be
presented using mercury as an example. Similar physics applies to the case of neon. You
are encouraged to do the neon experiment first since the experiment on mercury has a
longer start-up time due to the need for temperature regulation.
Energy Levels in Mercury
A mercury atom has 80 electrons. For an atom in the ground state the K, L, M, and N
shells of mercury are filled and the O and P shells have the following electrons:
O shell: 5s2, 5p6, 5d10
P shell: 6s2
Figure 1 Energy levels of mercury that are relevant to this experiment. Energy level
separation in electron volts is indicated on the right.
.
Energy levels in mercury, which are relevant to this experiment, are shown in Figure 1.
The energy levels are labeled using two notations.
nl, where n is the principle quantum number and l is the orbital angular momentum
quantum number, designated by s (l = 0) and p (l = 1).
2S+1
LJ , where S, L and J are the total spin quantum number, total orbital angular
momentum quantum number, and the total angular momentum quantum number.
The 1P1 and 3P1 are ordinary states having lifetimes of about 10 -8 s before decaying to the
1
S0 ground state by photon emission. The 3P2 and 3P0 are metastable states, having
lifetimes of about 10-3 s or about 105 times as long as an ordinary state. Hence, the
probability per second of an electron making a transition from either the 3P2 or the 3P0
state to the 1S0 ground state by photon emission is 105 times smaller than the transition
from either the 3P1 or 1P1 to 1S0. Thus the transitions from 3P2 and 3P0 to 1S0 are
forbidden transitions, while the transitions from 3P1 and 1P1 to 1S0 are allowed
transitions. The allowed transitions for photon emission are indicated by the two arrows
on the left in the figure, and the four arrows on the right indicate energy spacing in units
of electron volts. Direct excitation of 3P0, 3P1, and 1P1 from 1So by electron impact is
essentially equally probable.
Atomic Excitation by Inelastic Electron Scattering
An electron traveling from the cathode k toward the anode A has a mean free path l given
by
1
l?
2?nRO2
Where R0 = 1.5 x 10-10 m is the radius of a mercury atom and n is the number of atoms
per unit volume. At the end of one mean free path the electron has gained a kinetic
energy K from the electric field E
K = eEl
Where e is the electron charge and E is the electric field established by the accelerating
voltage Va. If l is long, then K will be large. The number density n is very sensitive to the
tube temperature; therefore l and hence K are very temperature sensitive.
Pre-lab Exercise 1: What is the mean free path l of an electron in a Franck – Hertz tube
heated to 373 K? 423 K? 473 K? Assume the gas of mercury atoms behaves as an ideal
gas. Use the following table of vapor pressure of mercury:
T (K)
399
457
501.8
534.7
596
630
P (mm Hg)
1
10
40
100
400
760
(CRC Handbook of Chemistry and Physics)
When an electron of kinetic energy K approaches a mercury atom with K< 4.6 eV, the energy difference between the first excited state and ground state, then the collision is elastic. In an elastic collision the electron loses some kinetic energy determined by the laws of conservation of momentum and kinetic energy. Pre-Lab Exercise 2: The loss of kinetic energy by an electron when it collides elastically with a mercury atom is greatest when the collision is head on. For an elastic head on collision with the mercury atom, assumed initially at rest, show that the change in electron energy is given by ?K ? 4mM ?m ? M ?2 KO Where m and M are the masses of an electron and a mercury atom and K 0 is the initial electron energy. What is the fractional loss of kinetic energy by the electron for such a collision? Figure 2. The electrodes in the Franck – Hertz experiment. Coaxial cylindrical configuration. (Electrodes in our lab experiment are planar.) From your answer in Exercise 2 it should be clear that the loss of electron energy due to a single elastic collision is negligibly small. The probability of an inelastic collision occurring is large when the electron’s energy equals the energy difference between an excited state and the ground state of the mercury atom, that is 4.6, 4.9, 5.4, and 6.7 eV. At some radial distance r1 ? ?r from the cylindrical cathode k, the kinetic energy K of the electron will equal 4.6 eV and the first inelastic collision occurs. An arbitrary r 1 is shown in Figure 2. The inelastic collisions occurring in the cylindrical shell of radius r 1 ? ?r populates the 3P0 metastable state of the mercury atoms in the shell. The electrons that later enter the shell will collide elastically with the mercury atoms that are in the 3P0 state; hence, these electrons pass through the shell with negligible energy loss. At some later radius rE ? ?r, these same electrons will have a kinetic energy of E = 4.9 eV and they collide inelastically with mercury atoms in the ground state. The 3P1 state decays to the 1 S0 state after about 10-8 s by photon emission and then the atom is ready for another inelastic collision; that is, the atoms in the shell continuously convert electron kinetic energy to radiant energy. If the accelerating voltage V a is high enough, this process may be repeated in cylindrical shells of radii r 1E ? ?r, r2E ? ?r, …. Note that rE, r2E, and so on are the distances of travel required for an electron to gain a certain energy. What effect do these inelastic collisions have on the current measured by the picoameter in our experiment? The decelerating voltage Vd is 1.5 V and as Va is increased from 0V a current is first observed when Va exceeds 1.5 V and the observed current will increase as Va increases until Va = 4.9 V. When Va = 4.9 V, the electrons lose energy from inelastic collisions; hence they no longer have enough energy to overcome the 1.5 V decelerating voltage and the observed current decreases. As Va is increased from 4.9 V the current will again increase until Va = 9.8 V, which corresponds to a second cylindrical shell a distance of r2E ? ?r from the cathode where inelastic collisions which populate the 3P1 state occur. Thus when Va = n x 4.9 V, n = 1, 2, 3, … there is a decrease in current. A curve of expected current I versus Va is sketched in Figure X. Each peak represents the onset of inelastic collisions that populate the 3P1 state. The first peak does not occur at 4.9 V because of the contact potential difference between the cathode and anode. Figure 3. Measured current as a function of the accelerating voltage Va Procedure: The experiment with Ne tube should be done first, since it does not require heating. Mercury: 1. In your experimental set up the mercury tube is placed into the oven and needs to be heated to 180 C. The temperature of the oven is measured using a thermocouple and controlled by a temperature controller. Switch on the temperature controller and set up desirable temperature. Wait for temperature to stabilize. (It could take up to half an hour.) 2. Make the connections in accordance with the following drawing. (Vacuum tube leads and power supplies are marked according to the drawing.) Familiarize yourself with the instruments. When you have finished, have the instructor check your connections BEFORE you turn on the power. U2 U1 U3 U2 – is provided by HP6633A power supply Figure 4. Schematic diagram of the Franck – Hertz tube for mercury. 3. After the tube has been heated up for about ½ hour, the cathode heating should be switched on (f - fk). Use gray homemade power supply for the heating voltage, U1 and U3. 4. After one minute, set the retarding voltage (U3) to approximately 1.5 volt. 5. Set the accelerating grid voltage (U2) to 30 V (push Vset 30, Enter), and slowly increase the grid (g1) voltage (U1) to 1.8 V. If the current increases rapidly up to a microAmp level, a gas discharge has taken place, and the grid voltage and accelerating voltage should be turned down immediately. The accelerating voltage should then be increased to 30 V again, and the grid voltage set to a voltage slightly less than that at which the discharge took place. 6. Collect the data (the output current vs. accelerating voltage) using a LabView program. Plot the output current vs. accelerating voltage. A series of maxima and minima should appear. What causes these extrema? Determine the voltages between minima, and compare with theory. Neon: 1. Make the connections in accordance with the following drawing. (Vacuum tube leads and power supplies are marked according to the drawing.) Familiarize yourself with the instruments. When you have finished, have your connections checked by the instructor BEFORE you turn on the power. 1. Cathode Heater 2. Cathode 3. Protective Cylinder 4. Control Grid 5. Accelerating Grid 6. Target Electrode 1. Tube Socket 2. Protective Spring 3. Connection for the collector 4. Principle Circuit Diagram 5. DIN socket for the connection cable 6. 4 - mm sockets for heating voltage ( Uf ) 7. 4 - mm sockets for control voltage ( U1 ) 8. 4 - mm sockets for accelerating voltage ( U2 ) 9. 4 - mm sockets for counter voltage ( U3 ) 10. BNC socket for connection of collector current f fk g1 g2 U2 is supplied by HP6633A and HP6632A power supplies U3 is supplied by HP6234A power supply U1 and Uf is supplied by gray homemade power supply Figure 5. Schematic diagram of Franck – Hertz arrangement for neon. 2. Set the accelerating voltage to approximately 70 V. (You have to use outputs of both HP6633A and HP6632A power supplies. How should you connect them: in series or in parallel?) 3. Switch on the heating current and let the cathode warm up for approximately 1 minute. Use gray homemade power supply for the heating voltage only. 4. Set the retarding potential (U3) to approximately 7 V. 5. Slowly increase the control voltage (U1) to approximately 1.5 V. In the process, observe the space between the control grid and the accelerating grid. The control voltage which is correct for the tube and the current cathode temperature is achieved when three (red colored) light bands can be observed. If the current increases rapidly, a gas discharge has taken place, and the grid voltage and accelerating voltage should be turned down immediately. The accelerating voltage should then be increased to 70 V again, and the grid voltage (U1) set to a voltage slightly less than that at which the discharge took place. Collect the data (the output current vs. accelerating voltage) using a LabView program. Obtain a plot of the collector current vs. accelerating voltage. Determine the voltages between minima and maxima. Explain your results. Data collection with LabWiew You may find the following hints useful: 1. Write a simple program to read the ammeter through the GPIB interface. ? Use Receive function to read the data. The GPIB address of the ammeter is set on the back panel in binary code. Try to read it. (For example, 1010 in binary is 1x23 + 0x22 + 1x21 + 0x20 = 10) 2. Write a program which ramps the output of the power supply U2. ? First, write a simple program to send a command to the (0 – 50 V) power supply. You would need to ramp the output of this power supply from 0 to 30 V for the mercury tube experiment, and from 0 to 50 V for the neon tube experiment. You do not need to ramp the other (0 – 20 V) power supply for the Ne tube experiment, since no maxima occur in this voltage interval. ? The GPIB address of the power supply can be read from the display. ? The appropriate command for setting the voltage of the power supply can be found in the power supply manual (see relevant pages of the manual in the PHYS341 binder). ? Use Send function to control the voltage of the power supply. What kind of wire is inputting the command to this function? Use Format Into String function to convert number into string and Concatenate Strings function to combine a constant Vset and a number (required voltage). 3. Combine (Use Stacked Sequence Structure: one frame sends command to the current source, another frame reads ammeter current. Place this structure in a While loop.) and modify these programs to take the current reading while ramping the voltage U 2, and save these data (voltage and corresponding current readings) into a data file (Set Loop Tunnels to enable indexing, use Built Array and Write To Spread Sheet functions). LabVIEW Measurement Writer_Version 2 Reader_Version 2 Separator Tab Decimal_Separator . Multi_Headings Yes X_Columns One Time_Pref Relative Operator mamoro4 Date ######## Time 13:45.9 ***End_of_Header*** Channels 2 Samples 61 61 Date ######## ######## Time 13:45.9 13:45.9 X_Dimension Time Time X0 0.00E+00 0.00E+00 Delta_X 1 1 ***End_of_Header*** X_Value Untitled Untitled 1 Comment 0 0 1.00E-13 1 0.5 1.00E-12 2 1 1.23E-11 3 1.5 5.01E-11 4 2 1.23E-10 5 2.5 2.52E-10 6 3 4.52E-10 7 3.5 7.36E-10 8 4 1.16E-09 9 4.5 1.74E-09 10 5 1.74E-09 11 5.5 1.45E-09 12 6 6.70E-10 13 6.5 6.38E-10 14 7 9.95E-10 15 7.5 1.61E-09 16 8 1.61E-09 17 8.5 3.57E-09 18 9 5.06E-09 19 9.5 6.84E-09 20 10 7.90E-09 21 10.5 5.40E-09 22 11 2.75E-09 23 11.5 2.17E-09 24 12 2.95E-09 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 12.5 13 13.5 14 14.5 15 15.5 16 16.5 17 17.5 18 18.5 19 19.5 20 20.5 21 21.5 22 22.5 23 23.5 24 24.5 25 25.5 26 26.5 27 27.5 28 28.5 29 29.5 30 4.30E-09 6.04E-09 8.24E-09 1.09E-08 1.40E-08 1.56E-08 1.33E-08 8.57E-09 5.59E-09 5.86E-09 7.66E-09 1.03E-08 1.35E-08 1.72E-08 1.99E-08 2.41E-08 2.45E-08 1.93E-08 1.93E-08 1.10E-08 1.24E-08 1.55E-08 1.97E-08 1.98E-08 3.08E-08 3.59E-08 3.98E-08 3.71E-08 2.89E-08 2.27E-08 2.20E-08 2.54E-08 3.10E-08 3.87E-08 4.81E-08 5.92E-08 Current (A) vs. acceleration Voltag 7.00E-08 6.00E-08 5.00E-08 4.00E-08 3.00E-08 2.00E-08 1.00E-08 0.00E+00 0 5 10 15 vs. acceleration Voltage (V) 15 20 25 30 35 LabVIEW Measurement Writer_Version 2 Reader_Version 2 Separator Tab Decimal_Separator . Multi_Headings Yes X_Columns One Time_Pref Relative Operator mamoro4 Date ######## Time 11:27.7 ***End_of_Header*** Channels 2 Samples 61 61 Date ######## ######## Time 11:27.7 11:27.7 X_Dimension Time Time X0 0.00E+00 0.00E+00 Delta_X 1 1 ***End_of_Header*** X_Value Untitled Untitled 1 Comment 0 1 2 1 9.00E-13 3 1.5 1.50E-12 4 2 1.30E-12 5 2.5 1.70E-12 6 3 3.00E-13 7 3.5 1.60E-11 8 4 7.27E-11 9 4.5 1.98E-10 10 5 4.25E-10 11 5.5 7.63E-10 12 6 1.24E-09 13 6.5 1.31E-09 14 7 3.94E-10 15 7.5 7.37E-11 16 8 3.20E-11 17 8.5 1.34E-10 18 9 4.02E-10 19 9.5 8.33E-10 20 10 1.49E-09 21 10.5 1.94E-09 22 11 3.30E-09 23 11.5 3.61E-09 24 12 1.97E-09 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 12.5 13 13.5 14 14.5 15 15.5 16 16.5 17 17.5 18 18.5 19 19.5 20 20.5 21 21.5 22 22.5 23 23.5 24 24.5 25 25.5 26 26.5 27 27.5 28 28.5 4.59E-10 1.48E-10 3.29E-10 7.69E-10 1.49E-09 1.49E-09 3.77E-09 5.22E-09 5.82E-09 4.12E-09 1.91E-09 1.85E-09 7.79E-10 1.28E-09 1.28E-09 3.50E-09 5.19E-09 7.17E-09 8.33E-09 7.49E-09 5.12E-09 3.09E-09 2.36E-09 2.56E-09 3.46E-09 5.02E-09 7.24E-09 9.92E-09 1.25E-08 1.39E-08 1.34E-08 1.18E-08 1.21E-08 Current (A) vs. Acceleration Voltage (V) 1.60E-08 1.40E-08 1.20E-08 1.00E-08 8.00E-09 6.00E-09 4.00E-09 2.00E-09 0.00E+00 0 5 10 15 20 25 30 LabVIEW Measurement Writer_Version 2 Reader_Version 2 Separator Tab Decimal_Separator . Multi_Headings Yes X_Columns One Time_Pref Relative Operator mamoro4 Date ######## Time 15:17.7 ***End_of_Header*** Channels 2 Samples 61 61 Date ######## ######## Time 15:17.7 15:17.7 X_Dimension Time Time X0 0.00E+00 0.00E+00 Delta_X 1 1 ***End_of_Header*** X_Value Untitled Untitled 1 Comment 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 0 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 10.5 11 11.5 12 1.00E-13 1.80E-12 1.00E-13 8.00E-13 1.20E-12 1.01E-11 7.79E-11 2.11E-10 4.50E-10 8.10E-10 1.34E-09 1.60E-09 7.09E-10 1.39E-10 4.19E-11 1.45E-10 4.35E-10 8.83E-10 1.50E-09 1.49E-09 3.24E-09 3.81E-09 2.19E-09 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 12.5 13 13.5 14 14.5 15 15.5 16 16.5 17 17.5 18 18.5 19 19.5 20 20.5 21 21.5 22 22.5 23 23.5 24 24.5 25 25.5 26 26.5 27 27.5 28 28.5 29 2.07E-09 1.72E-10 3.21E-10 7.30E-10 1.40E-09 1.61E-09 3.51E-09 4.88E-09 5.77E-09 4.53E-09 2.26E-09 2.24E-09 7.79E-10 1.21E-09 1.21E-09 3.22E-09 4.76E-09 6.52E-09 7.79E-09 7.41E-09 5.37E-09 3.24E-09 2.32E-09 2.41E-09 3.15E-09 4.47E-09 6.38E-09 8.73E-09 1.10E-08 1.23E-08 1.19E-08 1.04E-08 9.13E-09 9.18E-09 Current (A) vs. Acceleration Voltage (V) 1.40E-08 1.20E-08 1.00E-08 8.00E-09 6.00E-09 4.00E-09 2.00E-09 0.00E+00 0 5 10 15 20 25 30 35 ... 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