Frank-Hertz-Experiment
Christopher Bronner, Frank Essenberger
Freie Universität Berlin
September 30, 2006
Contents
1 Physical fundamentals
1
2 Tasks
3
3 Measurement protocol
3.1 Devices . . . . . . . . . . . . . . . . . . . . .
3.2 Assignment 4: Neon . . . . . . . . . . . . . .
3.3 Assignment 1: Mercury on the oscilloscope .
3.4 Assignment 2: Mercury on the chart recorder
3.5 Assignment 3: Temperature dependency . . .
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3
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4 Analysis
4.1 Neon tube . . . . . . . . .
4.2 Mercury tube . . . . . . .
4.3 Temperature dependency
4.4 Results . . . . . . . . . . .
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5
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9
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5 Discussion
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9
Physical fundamentals
Around 1911 James Franck (1882-1964; German Physicist) and Gustav Hertz
(*1887; German Physicist) worked on experiments to investigate the interaction
of electrons with gas molecules. They used a tube filled with mecury vapor in
which elektrones can be accelarated by a voltage U1 and before they hit the
anode they are slowed down by a voltage U2 ¿ U1 .
1
Figure 1: Frank-Hertz Apparatus
In the experiment they let the stopping voltage U2 constant and increased
the accelation voltage U1 . Then they measured the current between the kathode
and the anode. They got in prinziple this result:
Figure 2: I over U1 in prinziple
This lead to the conclusion, that there discrete excitation states for the
mercury atoms. At first the electrons are constandly accelarated an do elastic
collisions with the mercury atoms. So it is no problem for them to go through
the stopping voltage and the current is rising.
Then the kinetic energy of the electrons (Ekin e = e · Us ) reach the first
special energy level for the mecury atoms and they give up all there kinetic
energy two lift up the electron of the mercury atom to a higher level. Because
of their lose of energy the electrons can not pass the stopping voltage anymore
and the current breaks up. For every multiple integer of this energy the current
breaks aggain up.
When the stimulated mercury atom relax in thier normal level they emit
2
photons:
Ekin e
eUs
= Ephoton
= hν.
So the wavelenght of the emitted light is:
λ=
ch
.
eUs
The gas in the tube can be heated to decrease the free wavelenght of the
electrons. This is important because the likelihood that a electron hits a mecury
atom when it have the special energy value must be high. If this is not the case,
the current does not go down, because of electrons, which keep thier energy,
and can pass the stopping voltage.
In 1913 the existence of discrete excitation states in mercury was proved
thus verifying the quantum hypothesis and the Bohr-Sommerfeld model of the
atom (Niels Bohr; 1885-1962; Danish Physicist; Arnold Sommerfeld; 1868-1951;
German Physicist).
2
Tasks
1. Observing the electron collision-excitation curve (Franck-Hertz Curve) of
mercury at an oven temperature of about 190 ?C using an oscilloscope.
Optimizing the curve by adjusting various experimental parameters (oven
heating, cathode heating, accelerating voltage).
2. Quantitative recording of the curve with an XY-chart recorder. Determining the associated transition energy in mercury. Calculating the wave
length and frequency of the transition.
3. Observing and recording further excitation curves for temperatures of 130150 and 200?C. Qualitative discussion of the results.
4. Recording and evaluating a Franck-Hertz curve for neon at room temperature.
3
Measurement protocol
Tutor: Antonkin
Date: September 25, 2006
Begin: 14.30, End: 18.00
3.1
Devices
• Franck-Hertz tubes with neon and mercury vapor (the latter in an
oven)
3
• Operating units containing supply of heating voltage, accelerating and
decelerating voltages, amperemeter and the outputs for the chart recorder
and the oscilloscope.
• Multimeters VC 220
• XY-chart recorder
• Oscilloscopes
3.2
Assignment 4: Neon
Heating current: IH = 0.14 A (Voltmeter Error: ∆I → 1.2% ± 8dgt.
Acceleration voltage: UH = 70 V
We used the Franck-Hertz tube filled with neon gas. The measurement
was done by a computer interface which was connected to the operating unit.
We had to adjust the settings in the program to obtain a better picture but
the curve on the oscilloscope was completely satisfactory. In the program we
set cursors to determine the acceleration voltages of the minima and maxima.
We didn’t employ the origin of the graph because the voltage between it and
the first minimum is larger because it also contains the energy the energy the
electron needed to override the deceleration voltage.
Minimum
0
1
2
3
Maximum
0
1
2
UA /mV
930
2872
5041
7252
2045
3988
6198
Table 1: measurement for neon tube
3.3
Assignment 1: Mercury on the oscilloscope
Now we changed the setup and used the mercury tube. It was installed inside an
oven and was also connected to an operation unit. The operation unit itself was
connected to the oscilloscope and the XY-chart recorder. First we heated the
tube to 190 ◦ C. We then used the picture on the oscilloscope to get a typical
Franck-Hertz curve. Since we obtained it almost immediately, the setup
seemed to be working. We then used the oscilloscope to count the number of
maxima that the tube would deliver until it started to ionisize the vapor.
3.4
Assignment 2: Mercury on the chart recorder
Now we turned the XY-chart recorder on and calibrated it so that the graph
would have the right size on the paper. To determine the transition energy, we
4
recorded four different graphs. Allgraphs were recorded with an x scale of 10
V
V
cm and a y scale of 1 cm . The heating current was at IH = 0.31 A. We started
at an accelerating voltage of UA = 0 and increased until we saw the glowing of
the ionisized gas in the window of the oven. The voltage at which we stopped
the chart record was read from the multimeter and noted in the graph. In the
four records we changed the temperature:
ϑ/◦ C
190
130
210
210
Chart
1
2
3
4
Table 2: temperatures
The values read from the chart are marked on the graphs and will be discussed in the analysis.
3.5
Assignment 3: Temperature dependency
In this part, we investigated qualitatively the dependency of the Franck-Hertz
curve on the surrounding temperature. Therefore, we recorded five charts (No.
5-9) at temperatures of 143 ◦ C, 166 ◦ C, 170 ◦ C, 200 ◦ C and 225 ◦ C. We kept
the amplification of the output signal from the operating unit and the scale of
the recorder constant so that we would be able to compare the graphs directly.
Additionally, we had the information from assignment 2 where we also noted
the temperature. The graphs from assignment 2 can be used to investigate the
temp. dependency of the transition energy, those from assignment 3 serve to
determine the temp. dependency of the amplitude (therefore it was necessary
to keep amplification and scale constant).
4
4.1
Analysis
Neon tube
For the Fracnk Hertz experiment with the Neon filled tube we obtain:
i
1
2
3
4
5
Ui /mV
2211
2169
2542
2210
1943
Table 3: data for neon tube
5
Ū
=
5
X
Ui = 2, 2 mV
i=1
∆Ū
4.2
v
u 5
u1 X
= t
(Ui − Ū )2 = 0, 2 mV.
4 i=5
Mercury tube
For all measurement the error for U was obtained by a fixed error of ±2mm
plus the error of the multimeter:
∆U
∆U
∆L · κ = [0, 2mm + δU · 1cm] · κ
Umax 1, 2% + 0, 8V
= [0, 2cm +
· 1cm] · κ.
Umax
=
Umax
Where κ = L
and the maximal lenght must inserted in cm.
max
For the first measurement (T = 190◦ C) we get:
16, 9 cm=51,
ˆ
1 V ⇒ 1 cm=3,
ˆ 02 V.
i
0
1
2
3
4
5
6
7
Ui /V
11,5
16,6
21,8
26,9
32,1
37,2
42,3
47,4
∆Ui /V
0,9
0,9
0,9
0,9
0,9
0,9
0,9
0,9
Table 4: first measurement with T = 190◦ C
6
Figure 3: first measurement with T = 190◦ C
m = (5, 1 ± 0, 2) V
For the scond measurement we do not determinate a slope , because for the
(T = 130◦ C) low temperature we get only two peaks. For the third measurement
(T = 210◦ C) we obtain:
22, 6 cm=68,
ˆ
8 V ⇒ 1 cm=3,
ˆ 04V.
i
0
1
2
3
4
5
6
7
8
9
10
Ui /V
18,6
23,1
27,7
32,6
37,4
42,0
46,9
51,8
56,6
61,4
66,3
∆Ui /V
1
1
1
1
1
1
1
1
1
1
1
Table 5: third measurement with T = 210◦ C
7
Figure 4: third measurement with T = 210◦ C
m = (4, 8 ± 0, 12) V
For the last measurement with the same temperature as the third measurment (T = 210◦ C) we reduced the amplifying. We got:
21, 8 cm=69,
ˆ
4 V ⇒ 1 cm=3,
ˆ 18 V.
i
0
1
2
3
4
5
6
7
8
9
10
Ui /V
13,3
18,4
23,5
28,6
33,7
38,8
43,9
48,9
54,0
59,1
64,2
∆Ui /V
1
1
1
1
1
1
1
1
1
1
1
Table 6: last measurement with T = 210◦ C
8
Figure 5: last measurement with T = 210◦ C
m = (5, 1 ± 0, 1) V
4.3
Temperature dependency
For higher temperatures the amplitude decreases. Seen in the charts 5 to 9. Also
the point, when the mecury vapor starts to ionisize, moves to higher voltages.
Also this effect can be seen in the charts. The energy difference between two
maxima does not depend on the temperature.
4.4
Results
For the neon tube we obtain: EN e = (2.2 ± 0.2) eV
The weighted mean for mecury is: E = (4.97 ± 0.07) eV
5
Discussion
The experiment with the mercury tube can be regarded as successful. The
reference value for the transition energy of 4.89 eV is not within the tolerance of
our value of E = (4.97 ± 0.07) eV , but it is very close. The curves we obtained
on oscilloscopes and on the charts comply with the theoretical expectation.
The value of the transition energy of neon, EN e = (2.2 ± 0.2) eV , is far away
from the reference value of about 19 eV, but we don’t have any explanation
for such a large deviation. Perhaps, the voltage that was transmitted to the
computer was not the accelerating voltage but some other that was only proportional to it and we should have controlled starting and end value of it to
calculate the real voltage.
Our results for the dependency on temperature are also according to expectation.
9
During the corse of the experiment it was hard to keep the temperature
constant within the oven and there is no way to be sure that the temperature
at the thermometer is the same as the one inside the tube. Because of that,
it may be that the chart is stretched vertically in some way but that shouldn’t
have any effect on the values of the transition energies since we learned that it
is not depending on temperature.
The only sources of the errors in this experiment are the multimeter error
(which is quite large) and the error at reading the chart. Both were respected
in the calculation. The fact that the values for the energies are all too high
hints a systematic error. Maybe there were small amounts of other elements or
molecules inside the tube that have a stronger bond.
The initial energy of the electrons leaving the cathode is statistical and
should have a small effect beause of our many values.
What is absolutely clear aside from all values and error intervals is that the
energy levels in mercury and neon are not continuous but discrete. Therefore,
the experiment is confiming Bohr’s model of the atom in a very strong way.
10