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Physikalisches Anfaengerpraktikum
Franck-Hertz-Versuch
Ausarbeitung von
Constantin Tomaras & David Weisgerber
(Gruppe 10)
Montag, 24. Oktober 2005
eMail:
[email protected]
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(1) Introduction
To deliver the proof of a theory by "Townsend“, the German physicists Franck and Hertz
have experimented in Berlin since 1911 to examine collisions between electrons and gas
atoms. In their original work, they concluded that the measured 4,9eV must be the
ionization energy of the mercury gas.
After Nils Bohr commented this theory it was obvious that the electrons collided with the
mercury inelastic and it was possible to establish the link between the energy loss of the
electrons and the light emission of the gas which could be watched.
The illumination of the mercury came from electrons with a kinetic energy of more than
4,9eV and additionally a monochromatic radiation of 253,7nm could be measured.
This agreed to Einstein's formula:
E=h⋅f
E kin=e⋅U
⇒ h⋅ f =e⋅U
In the further process of the experiment, several other energy states of the mercury gas
were found.
(2) Experimental Overview
In a tube containing mercury gas (in order to vaporize the mercury, the tube was heated by
a surrounding oven at approximately 460K) electrons were accelerated by variable
potential between a heated cathode and an anode grid G. After passing the grid the
electrons are slowed down by a reverse potential until they hit the electron collector A. The
current of the electron collector is measured as a function against the acceleration
potential:
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The graph of the function current against acceleration potential is explained by the process
of inelastic collisions between the electrons and the heated mercury gas atoms inside the
tube. By being accelerated between the cathode and the anode grid the electrons collect
enough energy to energize a mercury gas atom which will afterwards lose its energy by
sending out a photon with the same energy as the electron lost by the inelastic collision.
Due to the (by Bohr's theory not answered) fact that atoms can only be energized by
discrete energies, the first possibility of the electrons to energize the mercury is at a kinetic
energy of 4.9eV.
If the electrons are not accelerated any more after the collision, they are not able to reach
the electron collector's cathode and the current at this cathode is decreased.
By rising the acceleration potential, it is possible for the electrons to do several inelastic
collisions which means that a local maximum of current at the electron collector can be
expected at voltages of n*4.9V.
In order to gain a better understanding of the whole physical effect this theoretical
overview shall be given:
(3) Theoretical Overview
To give a theoretical overview of the underlying atom model we start with the well-known
model of Rutherford:
It says that the atom consists of a positive charged core and several negative charged
electrons which are flying around the core on circular paths.
The Bohr model says that these electrons can only be found on discrete paths with
discrete energy values. It does not declare why the electrons do not send out
electromagnetic radiation according to Maxwell's equitations. This phenomena can only be
declared with the model of quantum physics. To describe the effects we found in this
experiment we do not need an insight view into the model of quantum physics (as this
would also go to far for this work) but we can examine the effects we found with the
postulates of Bohr:
(i) The angular momentum only assumes discrete values according to
L=r⋅m⋅v=
n⋅h
⋅
2
h⋅
2
n=1,2,3 , ...
On these discrete paths the electrons can be found. n is also known as the quantum
number.
(ii) Atoms can only be energized by discrete energy values: If an electron is changing its
course radius (where only discrete course radial are allowed) it emits a photon with a
frequency according to the lower potential and kinetic energy:
f=
 E a −E b 
h
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According to this formula, atoms absorb energy by increasing potential and kinetic energy
of electrons. As a result of the first postulate there can only be discrete energy values be
absorbed or emitted.
However, further explanations of the effects watched in this experiments can only be made
by using the model of quantum physics. At least with this underlying model, a theoretical
value of 4.9eV for the energizing energy of mercury could be calculated.
(4) Experiment
(i) Assembly
A scheme of the electric circuit of our experimental tube can be found in chapter 2.
In both experiments, with mercury gas and neon the wiring of the tubes and the measuring
devices was the same. In the experiment with mercury gas, the tube was heated by
approximately 460K to ensure that the mercury is in the state of gas.
The electron collector's cathode is connected to a small amplifier. The signal of this
amplifier is connected to the vertical input of our oscilloscope. Between cathode and
anode grid was put on a varying voltage of 0V to 45V. This voltage was also connected to
the horizontal input of our oscilloscope.
In the experiment with the neon tube this voltage could vary between 0V and
approximately 80V.
(ii) Measurements with the mercury gas
By calibrating the heating of the cathode, the counter voltage between anode grid and
electron collector's cathode and adjusting the amplifier and the electron beam of our
oscilloscope we tried to find a graph with sharp maximums. In order to achieve this the
acceleration voltage was put to alternating voltage between 0V and 45V.
An imprecise draw of this graph can be found in our protocol block. This part of the
experiment was only thought to find good values for the counter voltage and the heating
voltage of the cathode so this drawing has no scientific relevance.
In order to gain the exact positions of the maximums of the electron collector's current we
used these values for counter voltage, temperature and maximum acceleration voltage:
U counter =2,08V
T =451K ... 464K
U acceleration , max =45V
In order to find a the maximums of the electron collector's current very precise we
connected an analogue voltage measurement device to amplifiers output and we used a
digital multimeter connected to the cathode and the anode grid to get precise values of the
acceleration voltage.
We measured these values:
Maximum (U)
Distance between
maxima
16.1V
21.1V
5V
26.2V
5.1V
31.2V
5V
4
36.2V
5V
42.1V
6.1V
That means that we get as an average of the distance of the maxima:
n
1
m= ∑ U x
n x=1
26.2V
maverage =
=5.2V
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We made these calculations for the systematic an the statistic error:
statistic error :
1
m1 = ⋅s
n
s=

n
1
⋅∑ U x −m2
n−1 x=1
m1=0.21V
systematic error :
m2=0.5V
total error :
 m=m1m2=0.71V
So our result for the average of the distance of the maxima with error is:
maverage =5.2V±0.7V
With this result we are able to calculate the wavelength of the photons which are emitted:
h⋅c

=237 nm±17 nm
E=5.2eV±0.7eV=
Our results of a distance between two maxima and the wavelength of the emitted photon
are with values of maverage =5.2V±0.7V and =237 nm±17 nm within the expected
theoretical values of 4.9eV and 253.7nm.
(iii) Measurements with the neon tube
The second tube we examined was filled with neon which we did not need to heat because
it is in the state of gas at room temperature. The process of the experiment was more or
less exactly the same like the process of the mercury gas tube. A little difference to the
mercury tube was the higher maximum voltage of the alternating voltage of 80V. With this
voltage we tried to find a graph with sharp maximums and got this value for the counter
voltage between anode grid and electron collector's cathode:
U counter =4.8V
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Exactly like we did with the mercury tube we found these values for the maxima of the
neon tube:
Maximum (U)
Distance between
maxima
18.7V
36.8V
18.1V
55.6V
18.8V
77.8V
22.2V
That means that we get as an average of the distance of the maxima:
n
m=
1
∑U
n x=1 x
1
maverage = ⋅18.1V 18.8V22.2V=19.7V
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We made these calculations for the systematic an the statistic error:
statistic error :
1
m1 = ⋅s
n
s=

n
1
⋅∑ U −m2
n−1 x=1 x
m1=1.27V
systematic error :
m2=1.0V
total error :
 m=m1m2=2.27V
So our result for the average of the distance of the maxima with error is:
maverage =19.7V±2.3V
With this result we are able to calculate the wavelength of the photons which are emitted:
h⋅c

=629 nm±54 nm
E=19.7eV±2.3eV=
The wavelength we found here does not exist. This 19eV transition consists of two
different transitions. The one is a 2eV transition and the other is a 17eV transition. So
there are two different wavelengths emitted.
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(iv) Wavelength measurement with a spectrometer
In order to measure the wavelengths emitted by the neon tube we use a classic optical
device, the pocket spectrometer. The scale of the spectrometer was calibrated using a
neon lamp and afterwards we measured the wavelengths of the photons emitted by our
neon tube with a precision of ± 5nm. We got the following values:
orange =620 nm±5 nm
 red =660 nm±5 nm
green =655 nm±5 nm
(5) Questions
(i) Explain the terms elastic collision and inelastic collision
An elastic collision is a collision in which the total kinetic energy of the colliding bodies
after collision is equal to their total kinetic energy before collision. Elastic collisions occur
only if there is no conversion of kinetic energy into other forms, as in the collision of atoms.
Inelastic collision is a collision in which some of the kinetic energy of the colliding bodies is
converted into internal energy in one body so that kinetic energy is not conserved. In
collisions of macroscopic bodies some kinetic energy is turned into vibrational energy of
the atoms, causing a heating effect
(ii) Why is an electron at energies below 4.9 eV only able to perform elastic collisions?
Electrons with energies below 4.9 eV are not able to perform inelastic collisions because
they do not have enough energy to energize the atom it is colliding with. In addition, the
mass of the atom is much bigger than the mass of a single electron so the collision can be
compared to a ball hitting a wall.
(iii) Why is the energy an electron can transfer to an atom low in elastic collisions?
Compared to an atom the mass of an electron is very low. The mass of a mercury atom is
200.59 u while the mass of an electron is only 5.48580⋅10−4 u .
(iv) How does an atom excited by an inelastic collision dispose itself of the acquired
energy?
The energy is emitted in form of a photon.
(v) What is the difference between the excitation of an atom by electrons and by light
quanta?
While electrons can loose just portions of their kinetic energy, light quanta are fully
absorbed by atoms. As a result of this, light quanta must match the difference between two
discrete energy values of an atom in order to energize it. If it does not match it will not be
absorbed.
(vi) Why is it necessary to apply a deceleration voltage between collector electrode and
anode grid?
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If no deceleration voltage is applied between electron collector's cathode and the anode
grid the maxima might not be very sharp. In addition, if electrons have just a low amount of
kinetic energy they will hit the electron collector.
(vii) Compare the functionality of a Franck-Hertz tube with that of a fluorescent lamp and
try to understand this lamp with the help of the schematic sketch. Why are these
lamps called fluorescent lamps? [cf. Bergmann-Schäfer, Lehrbuch der
Experimentalphysik,
vol. III (Optik)]
The common fluorescent tube relies on fluorescence. Inside the glass tube is a partial
vacuum and a small amount of mercury. An electric discharge in the tube causes the
mercury atoms to emit light. The emitted light is in the ultraviolet range and is invisible, and
also harmful to living organisms, so the tube is lined with a coating of a fluorescent
material, called the phosphor, which absorbs the UV and re-emits visible light.
(viii) What is the difference to an x-ray tube?
In a x-ray tube the high energy photons are emitted when the electrons hit the anode with
high kinetic energy while in fluorescent tubes the photons are emitted when the electrons
hit gas atoms.
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