Download Frank Hertz

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Umeå University
Department of Physics
Leif Hassmyr
2012-02-05
FRANCK-HERTZ EXPERIMENT
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The Franck–Hertz Experiment
Background of the Experiment
In 1912 Niels Bohr developed his model of the atom, in which electrons are allowed only
certain discrete orbits. Transitions between these orbits may take place only when the atom
absorbs or emits quantized packets of energy E = hc . This explains the spectral lines given off

by an excited element, such as described by Rydberg’s formula for the series of spectral lines
for hydrogen.
In 1914 James Franck (American (German-born) physicist, 1882-1964) and Gustav Hertz
(German physicist, 1887-1975, nephew of Heinrich Hertz, who discovered radio waves)
reported an energy loss occurring in distinct “steps” for electrons passing through mercury
vapour, and a corresponding emission of the ultraviolet line (λ=254 nm) of mercury. A few
months later, Niels Bohr recognized this as evidence confirming his model of the atom. The
Franck-Hertz experiment is thus a classic experiment confirming quantum theory and earning
them the 1925 Nobel Prize in Physics.
Task:
To perform Franck-Hertz experiment and from it determine excitation energy of mercury
(Hg) and neon (Ne).
Theory
The experiment is performed by electrons emitted thermally from a cathode filament (K).
Then they are accelerated between the cathode (K) and anode grid (A) using an applied
voltage, UB. Between the anode grid and the collector plate (M) is a low reverse voltage,
UM=1.5 V, to stop electrons whose kinetic energy is below a certain value.
The substance to be examined, in our case, mercury / neon, is contained in the tube in gaseous
form,. Current, IM from the collector plate (M) is studied as a function of the applied
acceleration voltage, UB. The curve thus obtained exhibits a series maxima and minima,
which must be explained.
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Fig. 1
Circuit diagram for the Franck-Hertz experiment
If the kinetic energy of the electrons is too small to excite the atoms in the vapour, the
electrons collide elastically and lose almost no energy, as required by the conservation of
energy and momentum, and a large current is detected at plate M. If, on the other hand, the
electrons gain just enough kinetic energy to equal the energy level transition of the atoms,
some will collide inelastically and transfer energy to the atoms. These electrons will not have
enough energy to overcome the retarding potential at plate M, and a smaller current will be
detected.
As the voltage is increased further, some electrons will transfer their energy to the vapour
early enough to be accelerated again to an energy eV0, and the current detected at M will
again increase until the next excitation energy threshold is reacted. This occurs at either the
energy of a different transition or twice the energy of the ground state transition. Measurement
of the differences in the accelerating voltage between the minima in the detected electron
current can be used to determine the first excitation level of mercury atoms.
As soon as the acceleration voltage increases above the brake voltage a current is flowing
from the final electrode This current will increase with increasing accelerating voltage. The
collisions that constantly take place between electrons and gas atoms are elastic and exert
very little energy loss for the electrons. At a certain critical value of a few volts however the
first excitation energy for the gas is reached. The electrons taking part in inelastic collisions
will not have sufficient remaining to reach the anode leading to a rapid decrease in current. By
further increasing the acceleration voltage, the electrons can again reach the anode and the
current is growing again. When the acceleration voltage gives the electrons a kinetic energy
equal to twice the excitation energy electrons can undergo two successive inelastic collisions
leading again to a current which is rapidly declining. Further increase of accelerating voltage
means that the electrons of the two energy losses are accelerated so much that they can reach
the anode. The current increases again. This process is then repeated for acceleration voltages,
resulting in three-and quadruple excitation energies.
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The kinetic energy of an electron that goes through the potential difference V
is eV and we get an excitation when :
eV = En-E0
Where En is the energy of the excited state and E0 is the energy of the ground state. This
equation can be compared with the Bohr equation:
hν = En-Em
where En and Em denotes two energy states. Then Em =E0 apply:
eV = hν
The atom remains in its excited state a very short time and then emits most energy in the form
of a light quantum with frequency ν.
Task l: Determine the excitation energy of mercury.
Apparatus
Franck–Hertz tube with connector panel (NEVA didactic )
Oven, capable of heating (200°C)
(Warning, outside of the oven is hot!)
Franck–Hertz power supply, (NEVA Betriebsgerät)
(swept 0–70 V UB and reverse voltage UG , with amplifier to boost the current detected at the
collector plate M)
1 BNC/BNC-cable and 4 banana plug cables to run from the power supply to Franck–Hertz
tube.
2 dual banana plugs to BNC adapters to run from the power supply to the Oscilloscope
Oscilloscope (Agilent Technologies DSO6012A)
Thermometer (200°C)
Connect them according to the following wiring diagram (Fig. 2).
Fig. 2 Circuit diagram for the Franck-Hertz experiment on Mercury (Hg).
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Fig. 3 Picture of equipment to determine the excitation energy of mercury, Hg
The experiment is then carried out as follows:
1.
2.
3.
4.
5.
6.
Turn on the oven and set the temperature to 170 - 180 °C. It takes about 15 minutes to
heat up the oven. Keep an eye on the thermometer. Do not let the temperature exceed
205 °C. (Warning, outside of the oven is hot!)
Turn on the power supply and set the acceleration voltage UB to 0 V. Switch "UB" in
setting
).
Set “Heizung”(heating of cathode filament, K) roughly in the middle.
Set the gain in the middle.
Set the reverse voltage on minimum.
Start the oscilloscope and press the “menu”-button to put the oscilloscope in x/ymode.(Fig. 4)
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Menu button
Gain x- & y-
Fig. 4
7.
8.
Set gain for x-channel (ch1) to 0,5V/cm and y-channel (ch2) to 2V/cm. (Fig.4)
Slowly increase the acceleration voltage, UB. On the oscilloscope, you will hopefully
get a curve of the electrode current as a function of UB/10.
9.
To get the best curve as possible, you can now fine tune the settings:
1. Varying the temperature of the gas.
2. Varying the temperature of the cathode filament (“Heizung”).
10.
When you are satisfied with the result, you can press the "Cursors" button and place
(x1) and (x2) with the knob to the left of the "Cursors" button to measure the
difference in the accelerating voltage between two successive reductions of the
current. (Fig. 5)
Cursors button
Knob
Fig. 5
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11.
You can save the curve to USB stick as a .csn-file or a .bmp-picture for the laboratory
report:
1. Place the USB stick in USB connector and press the “Save/Recall” button. (Fig. 6)
Save/Recall button
USB connector
Fig. 6
2. Press “Save” button. (Fig. 7)
3. Change format with “knob”.
Choose BMP file (24 bit) image file for picture or CSV datafile for x/y-file.
Knob
Save button
Fig. 7
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4. Press “Save to”. (Fig. 8)
5. Press “File Name”.
Change File Name with “knob”.
Knob
Save to button
Fig.8
6. Press “Press to save”. (Fig. 9)
Press to save button
Fig. 9
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7. Picture or data file of screen is saved on the USB stick with the chosen File Name.
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Question 1.
Question 2.
Question 3.
Question 4.
How do these changes in temperature alter the shape of the curve? Explain
why?
Determine the excitation energy of mercury from the curve! Which transition
corresponds to this energy? See energy level diagram for mercury, Fig. 13.
Explain the origin of the curves. Can you determine some more excitation
levels? Why not?
At sufficiently high accelerating voltage a new phenomenon arises.
What is it and how was it discovered?
In the gas tube the cathode-anode distance much is longer than the free middle
path length, while the anode-electrode distance is much shorter. Why is this
geometry chosen?
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Task 2: Determine the excitation energy of neon.
Apparatus
Replace the metal box from the previous experiment to the black cylinder containing neon
gas. (Warning, outside of the oven is hot!)
Make the connection in the same way as before but also connect a control grid (Steuergitter)
located between the cathode and anode. It controls the acceleration just after the cathode. (Fig.
10).
Control grid
A KH
,UG
,UB
ͦ Collector plate, Control grid (Steuergitter)
A=Anode grid, K=Cathode, H=Cathode heating, M=
Fig. 10 Circuit diagram for the Franck-Hertz experiment on Neon (Ne).
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Fig. 11 Picture of equipment to determine the excitation energy of Neon, Ne.
Fig. 12 Power Supply
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1.
2.
3.
4.
5.
Turn on the power source. Set UB to 0V.
Set “Heizung” (heating of cathode filament, K) on minimum. It takes about 1,5
minutes to warm the filament.
Set the gain (Verstärkung) on maximum.
Set the reverse voltage (Gegenspannung) (UG) 6-10V.
Switch "UB" in setting
).Slowly increase the acceleration voltage, UB. On the
oscilloscope, you will hopefully get a curve of the electrode current as a function of
UB/10. If the curve “goes out of range”, reduce the power gain.
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To get the best curve as possible, you can now fine tune the settings:
1. Varying the reverse voltage (Gegenspannung) between 6-10 V.
2. Varying the temperature of the cathode filament (“Heizung”).
7.
To save the curve you do the same procedure as in task 1. (10-11)
Question 5.
Question 6.
Question 7.
Determine now from the curve the excitation energy of neon! Which transition
corresponds to this energy? (See energy level diagram for Neon, Fig. 14)
Why can´t the excitation energy be determined solely on the basis of the first
minimum?
Study neon gas during the study. Is there any other method to determine the
excitation energy based on the same tests?
Fig. 13 Energy level diagram for Mercury (Hg)
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Fig. 14 Energy level diagram for Neon (Ne)
Good Luck!
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Umeå University
Department of Physics
FRANCK-HERTZ EXPERIMENT
Name: …………………………………..
Course:………………………………….
Supervisor:……………………………...
Approved ................................................. ..
CONTENTS:
Mercury:
Chart: The current as a function of UB/10
Estimated value of excitation energy
p. …
p. …
Neon:
Chart: The current as a function of UB/10
Estimated value of excitation energy
p. …
p. …
Answers to questions 1-7
p….