Download The Franck-Hertz Experiment (FHV)

Gruppe 8 (Monday)
Simone Lingitz; Sebastian Jakob
The Franck-Hertz Experiment (FHV)
Group 8
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Gruppe 8 (Monday)
Simone Lingitz; Sebastian Jakob
1 Introduction
The Franck-Hertz Experiment is one of the basic experiments to determine the atom’s
structure. It shows, that electrons only can move around the atomic nucleus on certain orbits
and gives a magnitude for the binding energies of the outermost electrons.
The experiment uses the circumstance that bound electrons can be excited by inelastic
collisions into a higher unoccupied orbit. Only certain orbits can be occupied by the electrons,
further information hereof can be won from the Bohr model of the atom. When an electron
moves from a higher energetic state to a lower one, a spectral line of a certain frequency
(depending on the freed energy) is emitted.
Bohr’s theory can directly be proven by the Franck-Hertz Experiment.
2 Basics of the experiment
In a tube filled with mercury vapour (later in the experiment neon) are two electrodes
(cathode, anode). The cathode is heated, so there is electron emission, the anode is a grid, and
so electrons can pass it. There is also a collector installed, so the electrons, that have passed
the anode can be registered. Between collector and grid there is a small voltage, reversed to
the accelerating voltage. The emitted electrons of the cathode are accelerated by a voltage
between the two electrodes. On their way they collide with the gas atoms, but lose only a
small part of their energy, so they still can overcome the reverse voltage and make their way
to the collector. By rising the accelerating voltage, the electrons gain more energy. If now a
certain state of energy is reached, a collision of electron and atom causes a bound electron of
the atom to rise from its current energy state to the next one possible gaining the energy that
the colliding electron loses. The remaining energy of the electron now is too low to reach the
collector. If the acceleration voltage is again increased the energy of the electrons doesn’t fit
the atom’s electron’s energy demand and a collision will not set the orbital electron to a
higher state of energy, the electron again reaches the collector. This behaviour can be seen for
any rising voltage. As the current into the collector is measured as a function of the
accelerating voltage, the graph of this function is rising until the energy to excite an electron
is reached, then is strongly decreasing, to rise again, after this energy-level is passed. So the
graph’s maximal values show the amount of energy that is needed to excite an electron to the
next higher energetic state.
3 Experiment
3.1 Experimental assembly
Common to both experimental assemblies are the following components and their wiring:
The Amplifier for the collector is connected to the tube and ground, its signal is sent to the
oscilloscope as the vertical component. Anode and cathode are connected to a voltage source
(rage 0 to 45 Volts), which is also connected to the ground (same potential). The voltage
between the two electrodes is connected to the oscilloscope’s input (horizontal). The cathode
is heated by an adjustable voltage source so the cathode emits electrons. All mentioned
components (except those of the tube) are summed up in one device.
In the mercury-experiment the tube is heated by an oven to reach the right working
temperature.
In the neon-experiment only the tube is changed.
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Gruppe 8 (Monday)
Simone Lingitz; Sebastian Jakob
3.2 Mercury measurements
The following measurement values were won by moving in x-direction on the oscilloscope
and noting down when the curve reached a maximum or minimum value:
UB [V]
Maxima
Distance
Minima
Distance
Mesurement I
11,8
16,3
4,5
14,1
19,2
5,1
21,6
5,3
25,6
4,0
24,0
4,8
28,3
4,3
From this values a mean value of voltage difference (“Distance”) can be archived:
1 n
m = ∑U x
n x =1
1
mMesurement I = (4,5 + 5,3 + 4, 0 + 5,1 + 4,8 + 4,3)V = 4, 7 V
6
The statistical error has to be calculated by:
t
u1 =
s
n
1 n
(U x − m) 2 = 0,38V ; n = 6 ⇒ t = 1,11
∑
n − 1 x =1
So in the end we get a value for the statistical error:
⇒ u1 = 0,17V
For this we need the standard deviation s =
The systematic error is u 2 = 0,5V
From u1 and u2 the total error can be calculated as u = u1 + u 2 = 0,67V .
The wavelength can be found by using the following law:
E = (4,7 ± 0,67) eV
E=
h.c
λ
⇒λ =
h.c 4,136.10 −15.2,9979.10 8
=
= 264 ± 38nm
E
4,7 ± 0,67
The result from our measurement is 4,7 ± 0,67V for the voltage and 263,8 ± 38nm for the
wavelength. This means, that the theoretical values of 4,9V and 253,7nm are within the
precision range of our experiment.
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Gruppe 8 (Monday)
Simone Lingitz; Sebastian Jakob
3.3 Neon measurements
These values were measured in the same way as in 3.2.
UB [V]
Maxima
Distance
Minima
Distance
Mesurement II
19,0
36,0
55,0
78,0
17,0
19,0
23,0
0,0
25,0
42,0
63,0
25,0
17,0
21,0
The mean value of measurement II:
1 n
m = ∑U x
n x =1
1
mMeasuerement II = (17 + 19 + 23 + 25 + 17 + 21)V = 20,3 V
6
This formula was used for the statistical error:
t
u1 =
s
n
For its calculation the standard deviation is needed:
s=
1 n
(U x − m) 2 = 3,3V ; n = 6 ⇒ t = 1,11
∑
n − 1 x =1
Now we get the error’s value:
⇒ u1 = 1,5V
Together with the systematic error
u 2 = 1,0V
The total error comes to u = u1 + u 2 = 2,5V .
Energy and Wavelength are connected via this formula:
E = (20,3 ± 2,5) eV
E=
h.c
λ
⇒λ =
h.c 4,136.10 −15.2,9979.10 8
=
= 61 ± 7,5nm
E
20,3 ± 2,5
This wavelength does not exist, as the ~19V transition consists of a ~2V and ~17V transition.
So instead of one, two different wavelengths are emitted.
At the end of the neon experiment, the wavelength of the emitted light should be measured.
As the intensity of the neon tube’s light emission was too low, there were no spectral lines
recognized. Several attempts to find the spectral lines were made but only once there was
something to see, it was the complete red to yellow passage of the spectrum between the
wavelength of 500nm and 650nm nm.
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Gruppe 8 (Monday)
Simone Lingitz; Sebastian Jakob
4 Questions
4.1 Explain the terms collision and inelastic collision?
If the collision is inelastic, kinetic energy of the collision partners is “lost”. This “lost”
energy is converted to another form of energy, like deformation (heat) or excitation
energy. If the collision is elastic, the amount of kinetic energy before and after the
collision is the same and always constant.
4.2 Why is an electron at energies below 4,9eV only able to perform elastic collisions?
Electrons are only able to move on discrete orbits around the atomic nucleus. The
difference of energy of two orbits is 4,9eV (mercury). An electron can give its energy to
the atom and so the atom’s electron is able to lift to a higher orbit. This is an inelastic
collision. Below 4,9eV the electrons are only able to perform elastic collisions because
they have not yet the discrete energy that is necessary for an atom’s electron to reach a
higher orbit.
4.3 Why is the energy an electron can transfer to an atom low in elastic collisions?
The amount of transferred energy in a collision depends of the two collision partners’
mass, respectively their mass ratio (impulse!). If this ratio is 1:1, all energy can be
transferred. This is the case in straight collisions. If the ratio between the two partners is
very large, as in the case of an atom’s and an electron’s mass, the energy transferred is
very small.
me ⋅ ve = me ⋅ ve '+ m A ⋅ v A '
(Impulse)
1
1
1
2
2
2
(Energy)
me ⋅ ve = me ⋅ (ve ' ) + m A ⋅ (v A ' )
2
2
2
From this two formula results, that the speed of the electron after the collision is almost
the same (another direction), if the mass of the collision partner is much more higher than
the mass of the electron. And so almost no energy is transferred.
m − mA
m
ve ' = e
⋅ ve ≈ − A ⋅ ve = − ve
me + m A
mA
4.4 How does an atom excited by an inelastic collision dispose itself of the acquired energy?
An exited electron drops back to a lower energetic level. The difference of energy is
emitted in form of light quanta that can see as spectral lines (discrete wavelength).
4.5 What is the difference between the excitation of an atom by electrons and by light quanta?
The difference between both is the amount of its energy that can be transferred. A light
quanta can only be absorbed, this means it can only lose (transfer) its complete energy.
For this reason only light quanta of a certain wavelength (=energy) can excite an orbital
electron, so it moves to a higher orbit. In an atom-electron collision any part of the free
electron’s energy can be transferred to the atom; if this energy reaches the amount that is
needed to move an orbital electron to a higher orbit, the orbital electron makes the “jump”
into a higher orbit (inelastic collision). If the energy is not reached, the collision only
remains an elastic collision, without an orbital electron to jump.
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Gruppe 8 (Monday)
Simone Lingitz; Sebastian Jakob
4.6 Why is it necessary to apply a deceleration voltage between collector electrode and anode
grid?
The deceleration voltage is kind of barrier for very slow electrons, so only electrons above
a certain energetic can pass it. Without this speed filter it would be impossible to
distinguish between electrons that have collided with atoms and the ones that have not. So
only the electrons that are suitable for the experiment are registered, which makes it
possible to determine the maximum and minimum values of the graph and so the levels of
energy that excite orbital electrons.
4.7 Compare the functionally 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 those lamps called
fluorescent lamps?
In both cases the recognized light comes from excited electrons, falling back to a lower
energetic orbit. The differences between Franck-Hertz tube and fluorescent lamp are that
the lamp is working with ions and produces the needed heat to keep the process running
itself (but it has to be started by a starter to reach the operating temperature of the
electrodes and ionisation voltage), while the tube needs to be heated. When the lamp is
running the electrodes emit the electrons for the lighting process; there is also no
deceleration voltage needed in the lamp, as its purpose is not the measurement of any
atomic behaviour.
4.8 What is the difference to an x-ray tube?
X-rays are created, when high-speed electrons (accelerated by high voltage) are fast
decelerated by a metal anode. There are no excited electrons involved in the creating
process.
In opposite to the Franck-Hertz Tube (mercury!), the x-ray tube is evacuated, because any
collisions with atoms (goal in the Frank-Hertz Experiment) lower the electron’s energy
and so the efficiency of the x-ray tube.
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