“Modern Physics” Lab Report for the 2nd Year Undergrad Course in Physics
In this article we shall examine four different experiments under the title
“Experiments in Modern Physics”. These experiments include variations on historical and
famous ones, which date to the beginning of the twentieth century, and which paved the way
to the development of physics as we know it today. Some of the names involved are those of
Einstein, Franck and Hertz, Compton, and lastly a plethora of physicists who came up with
the underlying theory which brought to the experiment in thermionic emission. Ultimately
the four experiments discussed bellow are separate, yet they all lead to one coherent
conclusion: quantum theory and the theory of (special) relativity.
Authored by J. Shapiro and J. Zuta, instructed by Mr. Itay Asulin.
The Hebrew University of Jerusalem,
Faculty of Science,
Racah Institute of Physics,
Jerusalem 91904, Israel.
I. INTRODUCTION
It was a cloud of uncertainty that hogged around the subject of light and its
characteristics during the merry years of the beginning of the twentieth century. A
staggering amount of empirical evidence started to accumalate, most of which didn’t
fit together very well.
I. I. Photoelectric Effect
It appeared that if one was to expose a metallic surface to electromagnetic
radiation of sufficient frequency, electrons would be emitted. It has been suggested
that light comes in quantas which will be referred to as photons. Thus, the energy of
a photon “colliding” with an electron may then be absorbed by the electron in terms
of the electron’s kinetic energy. If the electromagnetic radiation (that is, the photons
carrying it) is below a certain threshold of frequency, then electrons would not be
emitted from the metallic surface. This is explained by the fact that it takes a
certain amount of energy to make the electron escape from the material, this
amount of energy will be referred to as the Work Function. Thus by conservation of
energy, we arrive at the notion that the maximal kinetic energy of the electron after
emission (denoted by E k ) from the material, would be the energy carried by the
photon (denoted by hν , where h is Planck’s constant and ν is the frequency of the
photon) minus the energy it took to escape from the material (denoted by φ ), or
mathematically
E k = hν − φ .
(1)
The fact that the photons’ energy is hν may appear like black magic here, but in fact
it is rather conspicuous once one considers the relativistic energy of a particle, given
by
E = m2c4 + p 2c2 .
(2)
It would be easy to think of a photon as having a mass of zero quantity, which
means its energy is simply E = pc , where p, the momentum (of a massless object
such as the photon) is given by
p=
h
λ
=
hν
.
c
(3)
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“Modern Physics” Lab Report for the 2nd Year Undergrad Course in Physics
From here it easy to see how the energy of the photon is indeed hν . This effect of
electrons being emitted from a material upon being radiated by electromagnetic
energy of sufficient frequency is named the Photoelectric effect, and had been
mathematically explained by Einstein1. Studying the phenomenon usuallly involves
taking a tube of vacuum which has an anode and a cathode in it and radiating it
with electromagnetic energy of different frequencies and intensities. The radiation is
directed at the cathode, which hopefullly will result in electrons being emitted from
it with kinetic energy towards the anode – that is, current in the tube. The two ends
of the tube are then connected to an electric circuit in which a voltage is applied in
order to prevent current from passing in the tube. The voltage that has to be applied
is usually denoted by Vstop . The electric-energy an electron obtains within an electric
field may be formulated in terms of its charge multiplied by the potential difference
which is the voltage. Thus we arrive with the relation
Vstop =
h
φ
⋅ν − .
e
e
(4)
I. II. Compton’s Scattering
Another interesting effect, named the Compton (see FIG. 5.) scattering, deals
with photons interacting with electrons in a material, which results in an increase in
wavelength to the photons. The amount the wavelength increases by is named the
“Compton shift”. One may think of the photons with energy hν as colliding with
electrons which are at rest during the collision. That is, the electrons’ initial energy
is simply mc 2 . By applying the laws of conservation of energy and those of
momentum (to two perpendicular axes separately), one may derive the amount of
shifted wavelength in electromagnetic radiation:
λ ′ − λ = h m c [1 − cos(θ )] ,
(5a)
e
where λ is the original incident wavelength, λ ′ is the shifted wavelength, and θ is
angle of scattering. In our experiment we mainly deal with scattering angle of 180° .
Thus we may already derive a formula for the shifted frequency:
ν '=
ν
2h
1+
⋅ν
me ⋅ c 2
.
(5b)
I. II
III. The FranckFranck-Hertz Experiment
The Franck-Hertz (see FIG. 4.) experiment confirmed Bohr's quantized model
of the atom by demonstrating that atoms could indeed only absorb (and be excited
by) specific amounts of energy (quanta). In this experiment, we deal with a tube
which has an anode and a cathode again. However, this time, the tube will not be
evacuated, but rather will contain a certain substance of which atoms are to be
excited. Such substance could be mercury. In addition to the two electrodes in the
two ends of the tube, there are two more grids - penetrable to electrons - one near
1
Einstein’s image will not be brought here due to its familiarity.
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“Modern Physics” Lab Report for the 2nd Year Undergrad Course in Physics
the cathode and one near the anode. The first grid, near the cathode, is held at a
higher potential than the cathode. The second grid is held at the same potential as
the first one, but is slightly more negative than the anode. In the experiment, we
connect the two ends of the tube to an electrical circuit. We gradually increase the
potential between the cathode and the first grid, which tears electrons away from
the cathode and accelerates them toward the first grid. Once the electrons have
passed the first grid, they “feel” zero electric field; however, they have kinetic energy
with velocity directed at the second grid. As they pass through the tube between the
first and second grid, they collide with mercury atoms. It appears that these
collisions can be either elastic (energy conserving), or plastic. In the elastic
collisions, the mass of the electron is negligible compared to that of the mercury
atom – hence it loses negligible amount of kinetic energy, and continues on its path
toward the second grid. However, inelastic collision may take place, if the electron
has sufficient amount of kinetic energy, an amount equal to 4.9eV (for mercury).
With that kinetic energy, the mercury atom absorbs all of the electron’s energy and
becomes energetically excited. After such collision, the electron remains with almost
zero kinetic energy, and has trouble reaching to the second grid and thus to the
anode. Even if the electron has some amount of remaining kinetic energy after the
collision, it will be decelerated upon arriving to the second grid. Thus only electrons
which did not collide at all are prone to actually reach the anode. If one was to plot
the potential between the cathode and the first grid (This difference will be denoted
by Vaccel . ) versus the current in the tube, it would come clear that the current rises as
Vaccel . does , however, within 4.9 V intervals, there are sudden drops in which there
is almost no current at all, and then as Vaccel . grows bigger, we see current again (see
FIG. 17. (d)). This experiment shows how the mercury atoms may only be excited by
specific amount of energy, no more and no less. Of course collisions of second-order
may take place, that is, an electron colliding with an already-excited mercury atom.
However, such second-order effects will be overlooked in our analysis, as they are
much less probable to take place. It is also possible to extract the CPD2 (Contact
Potential Difference) value for the cathode and the anode from the “ Vaccel . versus
current” graph. The CPD is the difference, in terms of energy, between an electron
which occupies a place in the cathode and one which resides in the anode. This
difference is generated by the two being connected in an electrical circuit (by wires).
If we bear in mind that it takes 4.9eV to excite a mercury atom, we can take the
voltage value of the first drop in the “ Vaccel . versus current” graph, and subtract
4.9eV of it. That subtraction result is going to be the energy it took to move an
electron from the cathode to the anode, which is exactly the requested CPD value.
Another manipulation with the Franck-Hertz experiment is to heat the
cathode and see what happens to the “ Vaccel . versus current” graph. We should expect
that as we heat the cathode, the mercury gas gets denser within the tube, and it is
more likely for atoms to collide with it. Thus, the hotter the tube is, the better
picture we shall see. Finally we can use the same setup in order to measure what is
the ionization potential for mercury. For that, we merely have to reverse the voltage
of the grids and see in which voltage there is a jump in the current. When suddenly
2
The actual components of the energy being measured include Fermi’s energy, the metal’s work function –
not only the CPD.
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“Modern Physics” Lab Report for the 2nd Year Undergrad Course in Physics
there is current, it means mercury atoms have become ionized by electrons which
have collided with them, and now the positive ions of the mercury are the current
carriers.
I. IV.
IV. Thermionic Emission
The last experiment to be discussed in this article is the thermionic emission
experiment. Again we take an evacuated tube3, in which we heat the cathode, which
provides the electrons within it with sufficient energy to overcome the cathode’s
work function. Thus a cloud of electrons is generated near the cathode. By
connecting the two ends of the tube to an electrical circuit with a source, we create
potential difference between the cathode and the anode which in turn drives the
cloud of the electrons toward the anode, and generates current in the electrical
circuit. One would expect that the bigger difference there is in potential between the
cathode and the anode, the higher the measured current will be in the circuit.
However, a simple relationship (such as Ohm’s law) of I ∝ V cannot exist in the
system since a cloud of electrons already occupies the tube and creates shielding. So,
we use the Child-Langmuir Law,
J =
2 ⋅ qe
1
⋅
⋅V 2 ,
2
9 ⋅π ⋅ d
me
3
(6)
(where J is the absolute value of the current density in the diode, d is the distance
between the two ends of the diode, V is the voltage between the two ends of the
diode, and qe , me are the charge and mass of the electron) which provides the
solution to the vacuum diode problem to conclude that the current will obey the
following relationship:
3
2
(7)
I ∝V .
This, assuming that there are no collisions of electrons within the tube, and that the
initial energy of the electrons is negligible, that is, all of the electrons’ kinetic energy
comes from the potential difference. Additionally, it is also evident that there is a
non-trivial relationship between the current in the tube and the temperature of the
cathode. This relationship is given by the Richardson-Dushman Equation:
φ
−
K B ⋅T
2
.
Js = A⋅T ⋅ e
(8)
Here, J s is the absolute value of the current (the saturated current, that is, the
current at very large potentials) density, T is the temperature of the cathode, A is
Richardson’s constant, φ (the energy it takes to pull electrons out of it) is the work
function of the cathode’s material, and K B is Boltzmann’s constant. Finally we shall
try to reinforce the Stefan-Boltzmann law regarding radiation of energy from a black
body. Stefan’s law postulates that
(9)
P = σ ⋅T 4 ,
3
Unlike usually illustrated, our tube has cylindrical geometry which means more of the electrons that get
emitted from the cathode actually reach the anode. A better geometry would’ve been a spherical one;
however, such was not available to us at the lab. It appears that spherical diodes are quite expensive.
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“Modern Physics” Lab Report for the 2nd Year Undergrad Course in Physics
where P is power per unit of area, σ is the constant of proportionality, and T is
the temperature. Since the tube is not a black-body, we have to add to it the energy
it receives from its environment:
I ⋅V
4 S
(10)
+ σ ⋅ T0 ⋅ A ,
SC
SC
is the surface of the cathode, S A is the surface of the anode, and T0 is
σ ⋅T 4 =
where SC
temperature of the environment.
II. APPARATUS
Most of the systems dealt with in this article are old. In fact, the brand name
and model number have been mostly worn off from the relevant stickers. Thus it
would be difficult to specify exactly what instruments we used in our exepriments. A
qualitative description will follow however.
II. I. Ph
Photoelectric Effect
Contrary to what was written in the preceding paragraph, the photoelectric
system is actually rather modern. It is a “Pasco h/e Apparatus” (see FIG. 8). The
light source used is a lamp of mercury. We use mercury because of its discrete
spectrum, which allows us to isolate discrete light frequencies. Adjacent to the lamp
is a diffraction grating. The grating is comprised of a grid of small slits which
diffract the light from the lamp into a diffraction pattern, in which every wavelength
has a maxima in a different angle, for a given order of maxima – much like a superprism (see FIG. 6). After passing the grating, we have a spectrum of light composed
of five distinct frequency: 0.519, 0.549, 0.688, 0.741, and 0.82 – all in units of peta
Hertz, each wavelength to be found in a different angle from the source. On the
other hand, a compartment of the photoelectric tube is to be found. This
compartment is comprised of a little hatch where light passes through, and on which
filters can mount. In it, a tube with an anode and a cathode lies. The light from the
hatch reaches the cathode. The tube itself has a small capacitance. The tube is
connected to an electrical circuit, and as light charges the cathode, the capacitor
becomes charged more until the voltage between the anode and cathode is
stabalized. This voltage is Vstop discussed in Section I. I. The electrical circuit in the
compartment also has a digital voltmeter which allows us to measure Vstop and a
button to zero the charge on the capacitor upon necessity. Different filters are used
to either purify the wavelength entering the tube, or manipulate the intensity of
light. The digital voltmeter is attached to a computer which can plot a graph of the
voltage on the tube versus time.
II. II. Compton’s Scattering
Here we use a Ge-Li detector (see FIG. 9.), attached to amplifiers, which are
attached to a micro-ace computer (which sorts pulses to 2048 different channels).
The basic function of this constellation is to specify how many electrons arrived at
the detector and at what energies. On top of the detector, we put three different
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“Modern Physics” Lab Report for the 2nd Year Undergrad Course in Physics
sources of Gamma radiation (which basically emit high frequency photons). The
three sources are 60 Co which emits two types of energies: 1.173 and 1.332 MeV,
137
Cs which emits 0.662 MeV, and lastly 241 Am which gives us 0.06 MeV. The
detector is attached to a computer which can plot a histogram of the incidence of a
given energy level. Additionally, we were provided with lead blocks and aluminum
surfaces of various geometries to play with.
II. II
III. The FranckFranck-Hertz Experiment
As mentioned in Section I. III., we use a tube filled with vapor of mercury in
this experiment. This tube is heated with an oven to temperatures of up to 200
degrees Celcius. Additionally we also hook up a computer to voltmeters which
provide us with readings on the voltage on the first grid and the current in the tube.
See FIG. 19 for specific details of how the electrical circuit has been attached
together.
II. IV. Thermionic Emission
The experiment in thermionic emission included an electrical circuit of a
certain degree of complexity. It was comprised of a diode (an evacuated tube with a
cathode and an anode, see FIG. 10.) connected to voltmeters (hooked up to a
computer), resistors, and a power source. The tube was heated using a separate
power source. The relationship (which was written on a piece of card-board lying
around near the diode) between the voltage of the heating power source and the
temperature of the diode is
T ≈ 171.428 ⋅
°K
⋅Vsource + 1700° K .
Volts
(11)
On a different piece of cardboard was written the length and diameter of the
filament (a cylindrical cathode), equal to 1.4 centimeters (length) and 0.125
millimeters (diameter). The dimensions of the anode (which possessed cylindrical
geometry as well) were no where to be found, and were thus left for our poor
estimation. Our estimation was that the anode has the same length as the cathode
(it wouldn’t make sense otherwise) and a diameter of approximately 6.9 millimeters
(measured with a caliber, with an error of about 10%, see the discussion below for
why the error on this value is so big). A solenoid was also at our disposal.
III. PROCEDURE
The four experiments spanned over the course of several sessions in the
laboratory. First we would arrive and hold a Colloquium in which we’d discuss the
various theoretical aspects of the experiments. Then we would conduct the different
experiments. Everything went pretty smooth, except for the thermionic emission
system which had gone bananas at us. Hence we had to wait for a couple of weeks
for it to be fixed, and then retry the experiment, which fortunately went well in the
end.
III.
II. I. Ph
Photoelectric Effect
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“Modern Physics” Lab Report for the 2nd Year Undergrad Course in Physics
We measure the different stopping potential on the tube (by first zeroing the
capacitor, using the built-in button, then releasing it and having the computer
measure the stablized voltage) with various wavelengths at different intensities.
First using no filter at all. By setting the photoelectric head (FIG. 7.) to different
angles (FIG. 8.) we achieve different wavelengths. We also made a measurement
with the light source turned off at all (expecting to capture the light of the room) and
also one with a LED source which had been taken from one of our key-bundle (see
FIG. 11). This LED source is said to potentially cause damage to the instruments
(according to Mr. Samuel Rubinstein, one of the lab instructors), so we terminated
that stage of experiment immediately after being given that information. Because
that measurement was done last in order, there is no danger of it affecting the
precedeeing ones.
III.
II. II. Compton’s Scattering
After turning on the system (the computer, the detector, and its amplifiers),
which had been set up for us prior to executing the experiment, we fetch a box of
radioactive gamma sources and place them on top of the Ge-Li detector. We then
capture a histogram with the computer of the amount of electrons that had been
detected for each energy value. We put each source (of the three) alone and make a
measurement. The next phase of the experiment is to put aluminum or lead between
the sources and the detector and see what happens.
III.
II. II
III. The FranckFranck-Hertz Experiment
Again, the system has been hooked up for us and all we had to do was turn it
on. After turning it on, we set the dial of the oven to 200 degrees Celsius and
gradually changed the power source's voltage on grid 1 to higher potentials. This
voltage was measured by an adjacent computer which also measured the current in
the tube. After doing that for a given temperature, we gradually lowered the
temperature of the oven and made the same measurements. Finally, we reversed the
electrical circuit so that we could measure ionization potential of the mercury vapor.
The reversed electrical circuit is illustrated in FIG. 20.
III.
III. IV. Thermionic Emission
The thermionic emission experiment procedure is rather straight-forward.
After having the system setup (this stage was done by the lab administrator), we
turn the system on (mainly the power sources and the computer with the voltage
sensors attached to it) and gradually shift the dial of the power source voltage from
zero Volts all the way through to almost 30 Volts. Then we remain with a graph of
power source voltage versus current in the diode (which is actually voltage on a
resistor connected serially to it). We make this measurement for different
temperatures. Setting the temperatures is done by shifting the dial of the separate
temperature power source, from about 4 Volts, all the way up to 5.6 Volts. We also
measure the current of the heating power source.
Finally, as has been suggested by one of the lab administrators (Mr. Solomon
something…), we took the solenoid, hooked it up to yet another power source (of
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“Modern Physics” Lab Report for the 2nd Year Undergrad Course in Physics
unmeasured voltage) and put it around the diode tube (see FIG. 12).
measured what is the current in the tube with the computer.
We then
IV. DESIGN
IV.
IV. I. Ph
Photoelectric Effect
After measuring the stopping potential for the various wavelengths and
intensities, we are left with an array of potential versus time graphs. The saturation
of the potential signifies the stopping potential which we seek. We have six graphs
for each wavelength (one with no filter at all, and five more for intensities of 20%,
40%, 60%, 80%, and 100% - we were expecting have the same result for no filter at
all and a filter of 100%, of course) and five wavelengths all together, hence we
remain with a total of 30 different graphs.
IV.
IV. II. Compton’s Scattering
A histogram of energy level incidence exists for each gamma radiation source
put on the detector, that is, three histograms. Additionally we also put shielding
lead and aluminum blocks, which resulted in more histograms, all in all, 16
histograms.
IV.
IV. II
III. The Franck
Franck-Hertz Experiment
For each temperature, we have a graph of the voltage on grid 1 versus the
current in the tube. All in all we have four measurements. We also have a
measurement of the grid's potential versus the current for the ionization potential
experiment.
IV.
IV. IV. Thermionic Emission
For each temperature, we have a graph of voltage of the power source, which
is basically the voltage on the tube, versus the voltage on a resistor connected
serially to the tube. The voltage on the resistor is analogous to the current in the
tube by Ohm’s law. We made several measurements for each temperature with
different resistors, and we also made measurements with different temperatures of
the same resistor. For each measurement we also wrote down the current of the heat
power source.
A graph of Voltage on tube versus current in it exists for when we put
a solenoid around the diode tube.
V. RESULTS
V. I. Ph
Photoelectric Effect
The results of our photoelectric experiment are shown in Table 1, FIG. 13,
and FIG. 14. As can be seen from FIG. 14, the value we received for Planck's
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“Modern Physics” Lab Report for the 2nd Year Undergrad Course in Physics
h
m 2 ⋅ kg
. Using the value of the
= (0.28161 ± 0.02876) ⋅10 -14 ⋅
e
sec⋅ Coulomb
m 2 ⋅ kg 5
electron's charge from literature4, we arrive at h = (4.5118 ± 0.4607 ) ⋅10 -34 ⋅
.
sec
constant is
Additionally, in FIG. 15 are the results for the extraneous measurements we have
made with natural light (that is, the mercury light turned off completely) and with a
LED light (see FIG. 11).
V. II. Compton’s Scattering
The histogram for Cesium emission is shown on FIG. 25. We scaled the
histogram so that the first peak would be where we said there would be emission, in
section II. II. That means, 0.06MeV. Then we set out to find what were the other
peaks which should be the Compton's scattering shift and a photoelectric effect of
the second order. The second order means that after a photon collided with an
electron and was shifted to some different wavelength, that photon would then
collide with another electron, and pass all of its energy to the electron, in a process
similar to the photoelectric effect. See Table 3 for our results.
Then we shielded the Cesium (we took the Cesium and not the other
materials because it had the brightest spectrum) with different widths of lead and
perspecs and studied its spectrum. The results are shown in FIG. 28, 29 and 30.
V. II
III. The FranckFranck-Hertz Experiment
The ionization potential measured for the mercury vapor located inside the
tube in our experiment was approximately (this was estimated by eyes) 9.3 Volts.
The value in the literature6 is 10.437 Volts. We then extracted from FIG. 17 the
differences between two drops of current in the tube, in terms of potential on Grid 1.
The results are shown in Table 2.
V. IV. Thermionic Emission
The measurements of the first phase of the experiment (Child-Langmuir
Law) are shown in FIG. 21. Notice how the current doesn't really go like the voltage
with a power of 1.5, but actually varies from 1.07 to 1.29, where the power rises as
the heating potential rises.
In FIG. 22. we have the results for the Richardson-Dushman part of the
experiment, where we calculated A (Richardson’s constant), φ (The work function of
the material), and K B (Boltzmann's constant). The value of A was found to be
A = (161714.93133 ± 29915.44673) ⋅
4
Ampere
(see note 5). If we use the literary value
m 2 ⋅ °K 2
1.60217646 × 10-19 Coulombs, taken from Google.com.
It should be noted here that the uncertainty value given by the ± sign is by no means an error value. It is
merely a statistical value of uncertainty given by the data analysis program which specifies what is the
maximal and minimal values of the statistic for which we can get the same correlation value for the line.
6
Taken from http://environmentalchemistry.com/yogi/periodic/Hg.html.
5
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“Modern Physics” Lab Report for the 2nd Year Undergrad Course in Physics
of
K B 7,
we arrive at the work function for the cathode which we calculated to be:
φ = (4.739± 0.044 ) ⋅ eV
.
The last phase of the experiment included the conservation of energy
equation which stems from the Stefan Blotzman law (Equation 10). The results for
this plot are shown in FIG. 23. From this graph we can extract the value of the
constant of proportionality, which is Stefan's constant, σ . We received that
σ ⋅ S C = (2.77 ± 0.0177 ) ⋅10 −13 ⋅
J
. Using our poor estimation of the surface of the
s ⋅ °K 4
cathode,
II.
from
section
σ = (5.03 ± 0.003) ⋅10 −8 ⋅
IV
we
arrive
at
the
value
of
σ,
J
(see note 5).
s ⋅ m ⋅ °K 4
2
Finally, look at FIG. 24 to witness how the current in the diode suddenly
drops as we apply magnetic field in the direction of the filament's axis.
VI. DISCUSSION
VI.
VI. I. Ph
Photoelectric Effect
A considerable deviation exists between the Planck constant we measured
and the value from the literature8 ( ∆h ≈ 1.6475 ⋅10 -34 ⋅
m 2 ⋅ kg
, where our value is the
sec
smaller one). This deviation cannot be explained by statistical uncertainty, thus, a
technical explanation must be postulated. First, what if the wavelengths specified by
the manufacturer (Pacson) of the apparatus are not really what they are? Let us
recall that the wavelengths are determined by going to different angles from the
lamp. Because a diffraction grating is put on the lamp (see FIG. 6) each
wavelength's maximal value should be on a different angle. However, this might
have changed with time as there might be fingerprints on the diffraction grating or
perhaps the specific wavelength's maxima is indeed at the specified angle, but
perhaps there were other wavelengths at this location which were neither in
maximum nor in minimum. These considerations however are merely speculative.
The major problem with our measurement would perhaps be the analysis of the
capacitor's voltage versus time graph. In this graph we had to estimate what was
the stable voltage to which the capacitor was charged to (see the black horizontal
line in FIG 13). But this was done merely with our eyes and a mouse-pointer. This
stage must've brought considerable error into the measurement. Each error in this
estimation of the stopping potential is accumulative to the last graph from which we
extract Planck's constant (FIG. 14). Lastly, from FIG. 14 we see that for the lower
frequencies there is some deviation upwards. This might be explained by the fact
that when we measured lower frequencies, sun-light from the room came into the
hatch since the filters were not completely insulating. Thus we see this shift to the
7
8
e⋅V
, taken from http://en.wikipedia.org/wiki/Boltzmann_constant.
°K
m 2 ⋅ kg
, taken from from Google.com.
h = 6.626068 ⋅10 -34 ⋅
sec
KB =
8.617 339 ⋅10 -5 ⋅
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“Modern Physics” Lab Report for the 2nd Year Undergrad Course in Physics
upwards only for lower frequencies, since the sun brings us ultra violet light. But
when we work with high frequencies that come from the lamp, their intensities are
much higher than the sun's and thus are the only ones determining the effect.
A constructive conclusion from this experiment is the fact that as we
heighten the intensity of the incident light on the cathode, the time it takes the
capacitor to charge is shorter (seen most clearly in FIG. 13. (e)). This is due to the
fact that the more intensity there is to the incident light, the higher the current is
inside the evacuated tube, and as the current is higher, it takes less time for the
capacitor to charge. It is thus reasonable to state that the current in the tube is
proportional to the amount of time it takes the capacitor to charge.
A third, somewhat exotic conclusion from our experiment comes from its last
stage. Examining FIG 15 we notice two things: The stopping potential for natural
light is higher than it is for a LED source, and the time it takes to reach saturation
with a LED is longer. This can be explained by the fact that when we made the
measurements with the natural light, the windows blinds weren't shut and thus
sun-light was able to come through into the photoelectric head (FIG. 7). It is sensible
to assume that while sun-light contains high frequencies of light such as ultra-violet
ones we're usually recommended to worry about, the LED provides a rather
monochromatic source of light of lower-than-ultra-violet frequency. Thus, lower
frequencies mean lower stopping potential. Additionally, the longer time until
saturation might be explained by the fact the LED light provides less intensity than
the natural sun-light, contradicting Mr. Samuel Rubinstein's warning which was
discussed in section III. I.
VI.
VI. II. Compton’s Scattering
Most of the observed values we received for the Compton's scattering energies
and 2nd order photoelectric effect meet the expected values (at least with differences
of up to 5%), as Table 3 shows. We did, however, run into some trouble when we
tried to look for the photoelectric effect of the 2nd order in the Cobalt spectrum. As
Cobalt emits two different energy values, it is expected to obtain two different values
for the 2nd order photoelectric effect. However, that was not the case. We received
one only one value in the histogram (see FIG. 26), which suggests that the detector
does not have the sufficient energy to differentiate between values of 0.244MeV and
0.214MeV (That is, 0.03MeV) and thus we see the two different peaks in one peak,
at the observed 0.223MeV (The values are taken from Table 3). The value of the 2nd
order photoelectric effect for Americium was disregarded as the source was found to
be of very low intensity. We postulate that has probably been laying around in the
lab for a long while (maybe 30 years) until we came around and used it and we
recommend its replacement.
One of the biggest pitfalls of our experiment was to distinguish between what
the capturing program in the computer calls "Real time" and "Live time". When we
asked the instructors, they were actually at a loss. The basic problem is this: we
want to measure emission of some material (such as Cesium) which is being shielded
by different obstacles. However, the only thing we remain at the end of the
experiment is the number of electrons which got to the detector for every amount of
energy. From that follows that the longer we leave the capturing program open the
higher amount of electrons that will arrive at any given energy level. So if we want
to check how the energy level changes with various shielding obstacles, we have to
11
“Modern Physics” Lab Report for the 2nd Year Undergrad Course in Physics
make sure that we leave the system capturing for exactly the same amount of time
for each different shielding obstacle. That is all fine and dandy, but we had two
different time parameters given to us by the program, one called "Real time" and the
other "Live time". What indicates the actual time that has elapsed since the
beginning of the experiment was unknown to us. We thought about reading the
instruction manual, however that document was unfortunately unavailable to us.
We were told by lab instructor Mr. Michael Dovrat that we should only look at the
"Live time". When we made the actual experiment we saw the two parameters
advancing differently as the energy shields varied. So we made some of our
experiments with constant "Live time" and some of them with constant "Real time".
For that reason we were unable to obtain sufficient data for how the intensity varies
as the width of the obstacle widens.
FIG. 28 reveals the bitter truth. We made measurements for three different
widths of lead for Cesium emission at constant "Live Time". It does not require great
observation skills to conclude that the number of electrons for each width is actually,
exactly the same (besides some experimental noise). This probably means that the
"Live time" is adjusted by the frequency at which electrons arrive at the detector. So
these three measurements in FIG. 28 are good as crap.
We were cautious enough to also make measurements with constant "Real
Time", which can be shown in the red and black lines of FIG. 29. As can be seen, the
more width the less electrons that arrive. Thus we conclude that "Real time" means
the actual physical time that has elapsed since the beginning of the experiment.
Also on FIG. 29 with blue color is shielding from perspecs. We can see that
the main photoelectric peak is at a different energy than for lead shielding. This
leads us to conclude that different materials change the emission spectrum of the
Cesium source. Either that or that we somehow miss gauged the three histograms.
Last is FIG. 30, showing perspecs shielding of different widths for Cesium. As
seen, the two lines (black and red) are virtually identical, suggesting that the
perspecs is penetrable to the radiation and barely affects the shifting – at least
compared to the lead. Perhaps it is since its atoms are light.
VI.
VI. II
III. The Franck
Francknck-Hertz Experiment
It appears that the value we have calculated for ionization potential differs
mildly from the one in the literature. Again, this could be explained mainly by the
coarse estimate we have done in determining the value. Notice (in FIG 16) how the
ionization potential is actually a continuous step. That made the estimation even
more difficult.
We were expecting the value of the average in Table 2 to be 4.9 Volts for all
temperatures. As the table exhibits, this is not the case. Not only did we get results
which differ from 4.9 Volts, but they are also different for each temperature. At least
the standard deviation in each temperature is not that big, suggesting that the
difference is relatively constant within a single measurement of some specific
temperature. The fact that the measurements vary for different temperatures might
be explained by the following possibilities: (a) As we raise the potential on Grid 1, it
gets heated and perhaps affects the overall temperature of the system – however,
this options is very unlikely, as the temperatures that Grid 1 must've reached to
were negligible compared to the 200 degrees Celsius which the whole system was
given to;(b) As we raise the temperature, some liquid atoms might be energetically
12
“Modern Physics” Lab Report for the 2nd Year Undergrad Course in Physics
excited (merely by the heating), thus when they collide with the electrons they are
already excited to the first, or perhaps second level and the electron needs to raise
them even higher, producing a different delta than 4.9 Volts;
VI.
VI. IV. Thermionic Emission
Our results for affirming the Child-Langmuir Law show that the current goes
like ~1.29 and not like 1.5 as the law actually indicates. This must rise from the fact
that we had to estimate where the saturation phase begins on the graphs (see FIG.
21. (e)) for instance. This estimation is of course prone to errors. Secondly, it is
possible that the diode is not completely evacuated, thus suggesting there are
collisions inside the tube which we didn't take into account.
There is a slight deviation in the Richardson's constant we have calculated
and the one given by the literature9 ( ∆A ≈ 1.04 ⋅10 6 ⋅
Ampere
= 86.54% ). This is
m 2 ⋅ °K 2
explained easily by the fact that in order to calculate the current density (the data
for FIG. 22) we have to use the definitions of the current density and current.
∫
Current density is defined as J ≡ ρ ⋅ v and the current is defined as I ≡ J ⋅ da . Our
S
computer measured the current, and not the current density. However, the
Richardson-Dushman equation relates to the current density. But how does one
derive the current density from the current itself? The task is practically impossible
since we do not know how the current distributes in all the space between the
cathode and the anode. Our best estimation was that the current density is uniform
(that estimation is actually rather poor since as we go along the radius of the
cylinder, there are less electrons for each unit of length), thus, I = S ⋅ J . But what
surface should we take for the calculation? The most reasonable assumption to use is
that since the electrons are being emitted from the cathode and it solely provides the
carriers of charge for the current (as comes evident from the saturation of current
predicted by the Child Langmuir law), the current density around the cathode is the
one to refer to, thus, we should take the surface of the cathode. But the surface of
the cathode was not given to us by the manufacturer, and it was also never written
anywhere. So we had to make more estimates. We measured the radius of the
filament (that is, the cathode) inside the diode and also its length and calculated its
surface as the surface of a cylinder. Of course those measurements were very prone
to errors as well. Given all those estimations and errors on the way, it is a wonder
we got to a deviation of merely 86%.
The material of the cathode inside our diode is tungsten. Its work function
(given by the literature10) deviates from the one we have calculated only slightly
(φ
9
10
≅ 0.2 ⋅ eV = 4.44% ) which is rather encouraging.
A = 1.20173 ⋅10 6 ⋅
φ ≅ 4.5 ⋅ eV
Ampere
, taken from http://en.wikipedia.org/wiki/Thermionic_emission.
m 2 ⋅ °K 2
, taken from http://en.wikipedia.org/wiki/Work_function.
13
“Modern Physics” Lab Report for the 2nd Year Undergrad Course in Physics
Lastly, the Stefan constant that we've measured differs only slightly from
the one given by the literature11 ( ∆σ = 0.64 ⋅10−8 ⋅
J
= 11.3% ). This deviation
s ⋅ m ⋅ °K 4
2
might be explained by the fact that in order to calculate this value, we had to divide
a value given to us by the fitting program by the surface of the cathode. It was
already postulated many times in this article that the surface of the cathode has a
very poor estimation, which will probably lead to this deviation in Stefan's constant.
Actually, this deviation is just 11%, which leads to the conclusion that our
estimation of the cathode's surface is pretty good after all, which could mean that
the error in the value of A (Richardson's constant) comes from the estimation that J
is uniform over all of the cathode's space and not from the estimation in the
cathode's surface.
It might appear peculiar that suddenly the current in the diode stops when
we turn on the voltage on the solenoid. However, a detailed explanation will follow,
which will make things a little bit clear. When we turn the voltage on for the
solenoid, a magnetic field is generated on it’s central axis, which is approximately
where the diode is located (FIG. 12). The direction of this magnetic field is on the
axis of symmetry of the cylinder that is the solenoid. If we denote this axis as ẑ ,
then the force on the electrons that are emitted from the cathode, with velocity in
the direction of the anode is given by the Lorentz force:
F = qe ⋅ E + v × B .
(12)
(
)
The electrical field between the anode and the cathode, generated by the power
source which is attached to them, is in the radial direction (cylindrical coordinates).
We also approximate that it is constant12. Thus we have:
F = m ⋅ a = m ⋅ vɺ = qe ⋅ [E0 ⋅ rˆ + B0 ⋅ (v × zˆ )].
(13)
Thus we arrive at three differential equations of first-order for the three cylindrical
components of the velocity:
m ⋅ (vɺr ⋅ rˆ + vr⋅ ⋅ vɺϕ ⋅ ϕˆ + vɺz ⋅ zˆ ) =
qe ⋅ [E0 ⋅ rˆ + B0 ⋅ (− vr ⋅ ϕˆ + vϕ ⋅ rˆ )]
or,
,
m ⋅ vɺr = qe ⋅ (E0 + B0 ⋅ vϕ )

 m ⋅ v r⋅ ⋅ vɺϕ = − qe ⋅ B0 ⋅ vr .

m ⋅ vɺ z = 0

(14)
(15)
The equations have the following solution (after applying some start-conditions on
the z-component):
11
12
σ = 5.67 ⋅ 10 −8 ⋅
J
, taken from http://en.wikipedia.org/wiki/Stefan%27s_constant.
s ⋅ m ⋅ °K 4
2
This approximation is actually not that reasonable since theoretically the electric field of a wire is
proportional to
1
. Since we also dealing with small lengths, this value may vary greatly.
r
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“Modern Physics” Lab Report for the 2nd Year Undergrad Course in Physics
2

qe
1  qe ⋅ B0  2
(o)
( 0)
 ⋅t
vr = vr + ⋅ E0 + B0 ⋅ vϕ ⋅ t − − ⋅ 
m
2  m 

q ⋅B

(0)
.
vϕ = − e 0 ⋅ t + vϕ

m

vz = 0



(
)
(16)
It can be seen from the solution that while the angular component of the velocity,
vϕ , is increasing linearly with time (or decreasing, but it doesn’t matter, it just
means that the angle of the velocity is changing clockwise or counter-clockwise with
time), its radial component (which signifies the velocity’s absolute value) decreases
with time. Thus upon being emitted from the cathode the electrons, force is exerted
on the electrons to return them back to the cathode and thus there is no current at
all.
VII. REFERENCES
[1] FIG. 1.
http://sol.sci.uop.edu/~jfalward/particlesandwaves/particlesandwaves.html
[2] FIG. 2. http://www.student.nada.kth.se/~f93jhu/phys_sim/compton/Compton.htm
[3] FIG 3. http://en.wikipedia.org/wiki/Franck-Hertz_experiment
[4] FIG 4. James Franck: http://www.britannica.com/nobel/micro/217_73.html
[5] FIG 4. Gustav Hertz: http://www.a-i-f.it/STORIA/Personaggi/Hertz.htm
[6] FIG. 5. http://www.th.physik.uni-frankfurt.de/~jr/physstamps.html
[7] FIG. 6. http://des.memphis.edu/lurbano/vpython/Education/edu_apps.html
[8] FIG 7.
http://store.pasco.com/pascostore/showdetl.cfm?&DID=9&Product_ID=1686&Detail=
1
[9] FIG 8. ftp://ftp.pasco.com/manuals/English/AP/AP-9368/012-04049J/01204049J.pdf
[10] FIG. 9. http://www.mhatt.aps.anl.gov/hutches/7idb/
[11] FIG. 10. http://www.tubecollector.org/grd7.htm
[12] FIG. 11.
http://www.amazon.com/gp/product/B00069ECRC/103-76177607263851?v=glance&n=3375251
15
“Modern Physics” Lab Report for the 2nd Year Undergrad Course in Physics
VII
VIII. FIGURES AND TABLES
FIG. 1. An illustration of the photoelectric-effect experiment.
FIG. 2. A schematic diagram of the Compton scattering.
FIG. 3. Electric Potential in a tube in the Franck-Hertz experiment.
16
“Modern Physics” Lab Report for the 2nd Year Undergrad Course in Physics
FIG. 4. James Franck (1882-1964), and Gustav Hertz (1887-1975) below him.
FIG. 5. A stamp illustrating Mr. Arthur H. Compton (1892-1962).
17
“Modern Physics” Lab Report for the 2nd Year Undergrad Course in Physics
FIG. 6. An illustration of the functionality of a diffraction grating used in the
photoelectric experiment.
FIG. 7. PASCO h/e Photoelectric Head (AP-9368).
18
“Modern Physics” Lab Report for the 2nd Year Undergrad Course in Physics
FIG. 8. “The h/e Apparatus Shown With the Accessory Kit and Mercury Vapor Light
Source” (taken from the Pasco’s user’s manual).
FIG. 9. Germanium-Lithium energy detector.
19
“Modern Physics” Lab Report for the 2nd Year Undergrad Course in Physics
FIG. 10. Ferranti GRD7 Guard Ring Diode.
FIG. 11. LED taken from one of our key-bundles.
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“Modern Physics” Lab Report for the 2nd Year Undergrad Course in Physics
FIG. 12. A variation on the thermionic experiment suggested by Mr. Solomon.
Freq.
Setup
20%
intensity
40%
intensity
60%
intensity
80%
intensity
100%
intensity
No filter
Average
0.519petaHertz 0.549petaHertz 0.688petaHertz 0.741petaHertz 0.820petaHertz
1.092
1.084
1.456
1.619
1.941
1.103
1.102
1.469
1.658
1.945
1.107
1.136
1.474
1.672
1.985
1.102
1.131
1.477
1.664
1.986
1.079
1.107
1.473
1.668
1.999
1.059
1.101
1.493
1.684
2.024
1.09
1.11
1.474
1.661
1.98
Table. 1. Stopping potential (in Volts) results for the photoelectric experiment.
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“Modern Physics” Lab Report for the 2nd Year Undergrad Course in Physics
Capacitor's Voltage Vs. Time for light of 0.519petaHertz
(charged by photo-electric current)
Capacitor's Voltage (Volts)
1.2
1.0
0.8
0.6
Legend:
Average Stopping Potential:
1.09Volts
0.4
20%
40%
60%
80%
100%
no filter
0.2
0.0
-2
0
2
4
6
8
10
12
14
Time (seconds)
FIG. 13. (a)
Capacitor's Voltage Vs. Time for light of 0.549petaHertz
1.3
(charged by photo-electric current)
Capacitor's Voltage (Volts)
1.2
1.1
1.0
0.9
0.8
Legend:
Average Stopping Potential:
1.11 Volts
0.7
20%
40%
60%
80%
100%
no filter
0.6
0.5
0.4
0.3
0.2
0
2
4
6
8
10
12
14
Time (seconds)
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“Modern Physics” Lab Report for the 2nd Year Undergrad Course in Physics
FIG. 13. (b)
Capacitor's Voltage Vs. Time for light of 0.688petaHertz
(charged by photo-electric current)
1.6
1.5
Capacitor's Voltage (Volts)
1.4
1.3
1.2
1.1
1.0
0.9
0.8
Legend:
0.7
Average Stopping Potential:
1.474Volts
0.6
0.5
20%
40%
60%
80%
100%
no filter
0.4
0.3
0.2
0.1
0.0
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
Time (seconds)
FIG. 13. (c)
Capacitor's Voltage Vs. Time for light of 0.741petaHertz
(charged by photo-electric current)
1.8
Capacitor's Voltage (Volts)
1.6
1.4
1.2
1.0
Average Stopping Potential:
1.661Volts
0.8
Legend:
0.6
20%
40%
60%
80%
100%
no filter
0.4
0.2
0.0
-0.2
0
2
4
6
8
10
12
Time (seconds)
FIG. 13. (d)
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“Modern Physics” Lab Report for the 2nd Year Undergrad Course in Physics
Capacitor's Voltage Vs. Time for light of 0.820petaHertz
(charged by photo-electric current)
2.2
2.0
Capacitor's Voltage (Volts)
1.8
1.6
1.4
1.2
Average Stopping Potential:
1.98 Volts
1.0
Legend:
0.8
20%
40%
60%
80%
100%
no filter
0.6
0.4
0.2
0.0
-0.2
0
2
4
6
8
10
Time (seconds)
FIG. 13. (e)
FIG. 13. (a),(b),(c),(d),(e): Voltage on the capacitor versus time on various
wavelengths.
Average Stopping Potential Vs. Frequency
2.2
2.0
Stopping Potential (Volts)
1.8
1.6
V_stop =(h/e)*Frequency - (Phi/e)
Parameter
-Phi/e
h/e
Value
-0.40944
0.28161
Error
0.17918
0.02876
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5
Frequency (petaHertz/10)
FIG. 14. Stopping potential versus incident light frequency in photoelectric
experiment.
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“Modern Physics” Lab Report for the 2nd Year Undergrad Course in Physics
Capacitor's Voltage Vs. Time for a LED and Natural light
Stopping Potential:
1.144 Volts
Capacitor's Voltage (Volts)
1.15
1.10
Stopping Potential:
1.05volt
1.05
1.00
0.95
Legend:
LED light
natural light
0.90
0.85
0.80
0.75
0
2
4
6
8
10
Time (seconds)
FIG. 15. Two extra measurements made in the photoelectric experiment for the
capacitor's voltage Vs. Time with no filters on the photoelectric head.
Current in tube Vs. Grid 1 Voltage
145 celscius degrees
Current in tube (Amp * 10^-8)
0.4
0.3
0.2
0.1
0.0
-0.1
0
2
4
6
8
10
12
14
Grid 1 Voltage (Accelerating Voltage) (Volts)
FIG. 16. Ionization potential for the tube in the Franck-Hertz experiment. The
measured value is 9.3 Volts for the ionization potential.
25
“Modern Physics” Lab Report for the 2nd Year Undergrad Course in Physics
Current in Tube Vs. Grid 1 Potential
160 celscius degrees
Current in Tube (microAmpere)
3
2
1
0
0
6
12
Grid 1 Potential (Volts)
FIG. 17. (a)
Current in Tube Vs. Potential on Grid 1
175 celscius degrees
Current in Tube (nanoAmper)
3.0
2.5
2.0
1.5
1.0
0.5
0.0
-2
0
2
4
6
8
10
12
14
16
18
Grid 1 Potential (Volts)
FIG. 17. (b)
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“Modern Physics” Lab Report for the 2nd Year Undergrad Course in Physics
E
1.0
Current in Tube Vs. Grid 1 Potential
190 celscius degrees
Current in Tube (nanoAmperes)
0.8
0.6
0.4
0.2
0.0
-0.2
-2
0
2
4
6
8
10
12
14
16
Grid 1 Potential (Volts)
FIG. 17. (c)
Current in Tube Vs. Grid 1 Potential
200 celscius degrees
Current in Tube (nanoAmperes)
0.6
0.4
0.2
0.0
0
8
16
24
Grid 1 Potential (Volts)
FIG. 17. (d)
FIG. 17. (a),(b),(c),(d): Franck-Hertz experiment results.
27
“Modern Physics” Lab Report for the 2nd Year Undergrad Course in Physics
2
Current in tube (n
anoAmperes)
Current Vs. Voltage Vs. Temperature
0
160
Te m
per 170
atu
re ( 180
Ce
lciu 190
sd
200
egr
ees
)
0
25
20 s)
t
15 (Vol
10 id 1
r
5
nG
o
ge
lta
o
V
FIG. 18. Franck-Hertz experiment meta-analysis of results.
Temperature
Place
(Celsius
Of Drop Degrees)
In Current
(Volts)
200
190
175
160
First drop
Second drop
Third drop
Fourth drop
Fifth drop
Sixth drop
Seventh drop
Eighth drop
Ninth drop
3.46
5.56
7.8
9.94
12.02
14.36
16.3
18.28
20.28
3.96
4.72
5.94
6.98
7.98
9.06
10
10.88
11.96
4.06
6.56
9.26
11.82
14.34
N/A
N/A
N/A
N/A
4
6.8
N/A
N/A
N/A
N/A
N/A
N/A
N/A
Average difference
2.1
1
2.57
2.8
Standard Deviation
0.127
0.131
0.078
N/A
Table. 2. Location of drops in the Franck-Hertz experiment. Notice how for each
temperature, as the order of drop rises, the difference shortens. This might be
explained by existence of second-order collisions.
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“Modern Physics” Lab Report for the 2nd Year Undergrad Course in Physics
FIG. 19. Franck-Hertz experiment circuit.
FIG. 20. Franck-Hertz experiment circuit for measuring ionization potential.
29
“Modern Physics” Lab Report for the 2nd Year Undergrad Course in Physics
Thermionic Emission; Heating Voltage of 4.4 Volts
Voltage on a serially connected resistor (Volts)
3.0
Vs=2.611v
2.5
2.0
1.5
Equation: V_diode=C*V_res^a+b
1.0
Chi^2/DoF
= 0.00531
R^2
= 0.98331
0.5
C
a
b
1.62755
1.07842
0.19567
±0.02561
±0.03826
±0.02449
0.0
-1
0
1
2
3
4
5
6
7
Voltage between the two ends of the tube (Volts)
FIG. 21. (a)
Voltage on a serially connected resistor (Volts)
Thermionic Emission; Heating Voltage of 4.6 Volts
4.0
Vs=3.709v
3.5
3.0
2.5
2.0
Equation: V_diode=C*V_res^a+b
1.5
Chi^2/DoF
= 0.00605
R^2
= 0.99097
1.0
C
a
b
0.5
1.77299
1.16837
0.25378
±0.02574
±0.02644
±0.02179
0.0
-1
0
1
2
3
4
5
6
7
8
Voltage between the two ends of the tube (Volts)
FIG. 21. (b)
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“Modern Physics” Lab Report for the 2nd Year Undergrad Course in Physics
Voltage on a serially connected resistor (Volts)
Thermionic Emission; Heating Voltage of 4.8 Volts
6
Vs=5.153v
5
4
3
Equation: V_diode=C*V_res^a+b
2
Chi^2/DoF
= 0.00708
R^2
= 0.99467
1
C
a
b
0
1.78984
1.18888
0.26125
±0.0252
±0.01785
±0.02031
-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0
Voltage between the two ends of the tube (Volts)
FIG. 21. (c)
Voltage on a serially connected resistor (Volts)
Thermionic Emission; Heating Voltage of 5 Volts
4.5
Vs=4.041v
4.0
3.5
3.0
2.5
Equation: V_diode=C*V_res^a+b
2.0
Chi^2/DoF
= 0.00368
R^2
= 0.99589
1.5
1.0
C
a
b
0.5
1.20759
1.22351
0.19207
±0.01638
±0.0149
±0.01334
0.0
0
2
4
6
8
10
12
Voltage between the two ends of the tube (Volts)
FIG. 21. (d)
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“Modern Physics” Lab Report for the 2nd Year Undergrad Course in Physics
Thermionic Emission; Heating Voltage of 5.2 Volts
Voltage on a serially connected resistor (Volts)
6
Vs=5.409v
5
4
3
Equation: V_diode=C*V_res^a+b
2
Chi^2/DoF
= 0.00428
R^2
= 0.99757
C
a
b
1
1.22192
1.23395
0.20074
±0.01429
±0.0101
±0.01257
0
-0.5 0.0
0.5
1.0
1.5 2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
Voltage between the two ends of the tube (Volts)
FIG. 21. (e)
Voltage on a serially connected resistor (Volts)
Thermionic Emission; Heating Voltage of 5.4 Volts
4.0
Vs=3.702v
3.5
3.0
2.5
2.0
Equation:V_diode=C*V_res^a+b
1.5
Chi^2/DoF
= 0.0018
R^2
= 0.99831
1.0
C
a
b
0.5
0.6693 ±0.00708
1.29758
±0.00782
0.07985
±0.00701
0.0
-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5
Voltage between the two ends of the tube (Volts)
FIG. 21. (f)
32
“Modern Physics” Lab Report for the 2nd Year Undergrad Course in Physics
Thermionic Emission; Heating Voltage of 5.6 Volts
Voltage on a serially connected resistor (Volts)
3.5
Vs=3.087v
3.0
2.5
2.0
Equation: V_diode=C*V_res^a+b
1.5
Chi^2/DoF
= 0.00104
R^2
= 0.99851
Const 0.51824
a
1.26167
b
0.15908
1.0
0.5
±0.00516
±0.00694
±0.00526
0.0
-0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5
Voltage between the two ends of the tube (Volts)
FIG. 21. (g)
FIG. 21.The voltage on a resistor connected serially to the tube versus the potential
between the two ends of the tube in the thermionic emission experiment.
Current Density vs. Temperature
1200
2
1000
2
J_saturation (Ampere * m )
J=AT exp(-Φ/(KBT))
800
R^2
= 0.99981
A
161714.93133 ±29915.44673
54999.92062 ±510.87928
Φ/KB
600
400
200
Measurements
0
2450
2500
2550
2600
2650
2700
Temperature (Degrees Kelvin)
FIG. 22. Equation 8, the Richardson-Dushman equation.
33
“Modern Physics” Lab Report for the 2nd Year Undergrad Course in Physics
Heating Power versus Temperature; Equation 10
4
Measurements
4
Equation: IV=(σ*SC)*T -σ*(T0)*SA
12
I*V = Heating Power (Watts)
R^2
= 0.99971
(σ*SC)
11
4
-σ*(T0)*SA
2.7756E-13
±1.7738E-15
-2.04042
±0.07302
10
9
8
7
2350
2400
2450
2500
2550
2600
2650
2700
O
Temperature ( Kelvin)
FIG. 23. Equation 10 put to the test. If our estimates for the surface of the cathode
are right, we get a pretty good measurement for the constant of proportionality, σ .
Current Vs. Voltage when applying a magnetic
field to the axis of the filament
Current through the diode (Amperes)
1.4
Measurements
1.2
Current before turning
on the magnetic field
1.0
0.8
0.6
Current after turning on the mag field
0.4
0.2
0.0
-0.2
1.2
1.4
1.6
1.8
2.0
2.2
2.4
Voltage between two ends of the diode (Volts)
FIG. 24. This is what happens to the Current vs. Potential graph under the
influence of a magnetic field to the axis of the filament which is turned on after the
existence of current, and then turned off.
34
“Modern Physics” Lab Report for the 2nd Year Undergrad Course in Physics
137
4000
Cs Histogram
6.62E5eV
3500
# of electrons
3000
2500
2000
1500
1000
3.21E4eV
500
4.68E5eV
1.96E5eV
0
-500
-100000
0
100000 200000 300000 400000 500000 600000 700000
Energy (eV)
FIG. 25. Histogram of Cesium 137 emission in the Compton's Scattering experiment.
60
10000
Co Histogram
1.173MeV
8000
Unexplained to us, maybe noise?
6000
1.11MeV
2000
0.223MeV
4000
0.957MeV
2nd order photo' effect
0.148MeV
# of electrons
1.332MeV
0
-200000 0
200000400000600000800000
1000000
1200000
1400000
1600000
1800000
2000000
Energy (eV)
FIG. 26. Histogram of Cobalt 60 emission in the Compton's Scattering experiment.
35
“Modern Physics” Lab Report for the 2nd Year Undergrad Course in Physics
241
Am Histogram
361.4eV
20000
3515.88eV
10000
Measurement
0.06MeV
# of electrons
15000
5000
0
-10000
0
10000
20000
30000
40000
50000
60000
70000
Energy (eV)
FIG. 27. Histogram of Americium 241 emission in the Compton's Scattering
experiment.
Histogram of Cs shielded by different widths of lead
All with the same Live time of 10seconds
250
# of electrons
200
150
small width
medium width
large width
100
50
0
-100000
0
100000 200000 300000 400000 500000 600000 700000
Energy (eV)
FIG. 28. Histogram of Cesium 137 emission shielded by three different widths of
lead, stopping the program at the same live time in the Compton's Scattering
experiment.
36
“Modern Physics” Lab Report for the 2nd Year Undergrad Course in Physics
# of electrons
137
Histogram of Cs shielded by different
materials of different widths
3600
3400
3200
3000
2800
2600
2400
2200
2000
1800
1600
1400
1200
1000
800
600
400
200
0
-200
Different energy
for the Photoelectric
effect
lead of certain width, real 49sec
lead of smaller width, real 49sec
perspecs, real 29sec
0
500
1000
1500
2000
Some arbitrary unit of energy
FIG. 29. Histogram of Cesium 137 emission shielded by two different widths of lead,
stopping the program at the same real time.
time. Additionally we put emission of Cesium
shielded by perspecs, with different real time. Done in the Compton's Scattering
experiment.
Histogram of Perspecs for Cesium 137 with the same real time
2500
# of electrons
2000
1500
1000
block in a lying position
block in a standing pos
500
0
0
500
1000
1500
2000
Energy of some arbitrary value
FIG. 30. Histogram of Cesium 137 emission in the Compton's Scattering experiment.
Shielding was done by a block of perspecs which was once put in a lying position and
once is a standing position.
37
“Modern Physics” Lab Report for the 2nd Year Undergrad Course in Physics
Material
Photoelectric
Energy
Expected
Compton
energy
Observed
Compton
energy
∆
Compton
Energy
Expected
2nd-order
photoelectric
energy
Observed
2nd-order
photoelectric
Energy
∆
2nd-order
photoelectric
energy
Cesium
0.662
0.477
0.468
1.9%
0.185
0.196
5.9%
Cobalt 1
1.173
0.963
0.957
0.6%
0.214
0.223*
4.2%
Cobalt 2
1.332
1.072
1.11
3.5%
0.244
0.223*
8.6%
Americium
0.06
0.00458 0.00351 23.4%
N/IA
~0
N/A
Table 3. Results from the Compton's Scattering experiment. All energy values are
given in units of MeV. The Cobalt 1 and Cobalt 2 materials signify the two different
wavelengths that Cobalt emits. * See section
38