Franck Hertz Versuch

Advanced Laboratory Course, Part I

Summer Term 2005

Report on

Franck-Hertz Experiment

Handed in byBenjamin Joachimi, Benedikt Klobes

Group β 10

Assistant: Svetlana Zinoveva18th February 2005

1

Contents

1 Introduction 3

2 Theory 3

2.1 Franck-Hertz tube . . . . . . . . . . . . . . . . . . . . . . . . . 32.2 Emission of electrons out of an heated cathode . . . . . . . . . 52.3 The mercury atom and transitions . . . . . . . . . . . . . . . . 52.4 Kinetic gas theory . . . . . . . . . . . . . . . . . . . . . . . . 72.5 Collisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.6 Two-phase system . . . . . . . . . . . . . . . . . . . . . . . . . 72.7 Photomultiplier . . . . . . . . . . . . . . . . . . . . . . . . . . 82.8 Interference-filter . . . . . . . . . . . . . . . . . . . . . . . . . 9

3 Setup of the experiment 9

4 Implementation and analysis 10

4.1 Proceeding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104.2 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114.3 Features of the Franck-Hertz curves . . . . . . . . . . . . . . . 124.4 Analysis of the Franck-Hertz curves . . . . . . . . . . . . . . . 124.5 Features of the photocurrent curves . . . . . . . . . . . . . . . 144.6 Analysis of the photocurrent curves . . . . . . . . . . . . . . . 144.7 Calculation of mean free path and collision time . . . . . . . . 15

5 Summary 17

6 Appendix 18

6.1 Table of data - calibration . . . . . . . . . . . . . . . . . . . . 186.2 Tables of data - Franck-Hertz curves . . . . . . . . . . . . . . 19

6.2.1 Databasis . . . . . . . . . . . . . . . . . . . . . . . . . 196.2.2 Interim results . . . . . . . . . . . . . . . . . . . . . . . 21

6.3 Table of data - photocurrent curves . . . . . . . . . . . . . . . 226.4 Legend concerning the original plots . . . . . . . . . . . . . . . 23

2

1 Introduction

In 1913 James Franck and Gustav Hertz demonstrated the possibility toprove the existence of discrete energy levels in atoms by means of atomic col-lisional processes. Thus the Franck-Hertz experiment combines the physicsof collision with the results of optical spectroscopy. Its result indicates thatatoms can only absorb a discrete amount of energy, regardless the way theenergy is transferred to the atom.

Using a setup similar to that of Franck and Hertz we will observe the quan-tized excitation of mercury atoms by means of electronic impact. We willmeasure the characteristic anode current and photocurrent for different setsof parameters like temperature and countervoltage. On the basis of this datawe will determine the excitation voltage of the 3P level of mercury.

2 Theory

2.1 Franck-Hertz tube

Figure 1: Franck-Hertz tube

The Franck-Hertz tube is a triode consisting of a cathode (K), an anode(A) and a grid-like electrode (G) between them. Figure 1 shows the arrange-ment of these components. The tube is filled with mercury vapour at lowpressure (about 10−2 mbar). The electrons emitted from the heated cathodeare accelerated between C and G by a voltage U ≡ UB. Thus they receivethe energy e · UB. The structure of the grid enables the electrons to reachthe actual experimental space in great number (otherwise they all would be

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captured by G). Between G and A a countervoltage ∆U ≡ UG is applied,which means that A is charged negatively in comparison with G. Thereforeonly electrons with energy larger than e · UG can reach the anode and causea current signal. If there was no countervoltage applied, all electrons wouldreach the anode and no modulation of the current signal could be measured.

Figure 2 displays a typical measurement of the anode current as a functionof the accelerating voltage. As soon as UB > UG the current increases withrising UB. But when it reaches a value UB ≈ 4, 9V (assuming UG << UB) itdecreases, forms a minimum and increases again to UB ≈ 2 · 4, 9V , then thisoszillation continues the same way. The interpretation of this observationsucceeds with the assumption that electrons of about 5 eV of kinetic energyundergo inelastic collisions with the mercury atoms and thus transfer theirenergy to a discrete excitation level of mercury.

Figure 2: Anode current curve

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2.2 Emission of electrons out of an heated cathode

The cathode in a vacuum tube can emit electrons if it is heated. Electronsin the conduction band of the cathode metal move freely within the bandbut cannot be released as they are held back by the Coulomb force of thepositively charged ion grid. In order to be emitted electrons have to overcomethe work function W of the order of a few eV. By means of additional thermalenergy due to the heating process electrons in the high-energy tail of theFermi distribution can be released. The share of electrons leaving the cathode

is governed by the Boltzmann factor e−

EkBT . When an acceleration voltage UB

is applied dragging the electrons away from the cathode, then E = W −eUB.Closer analysis of the emission process leads to the Richardson law

j = CT 2e−

W−eUBkBT (1)

where C is a material constant.

Around the cathode an electron cloud forms. This negative charge densityprevents the electric field built up by the acceleration voltage from reachingthe cathode, which results in a characteristic run of the vacuum tube currentwith voltage: I ∝ U

3

2 (Schottky-Langmuir-Formula, see also dotted line infigure 2).

2.3 The mercury atom and transitions

The mercury atom contains in total 80 electrons of which 78 are bound infilled states. In the ground state the two remaining electrons can be foundin the 6s state. Their spins of 1

2each can couple to a total spin of S = 0,1

leading to a singlet (multiplicity 1) and a triplet (multiplicity 3) state (see

figure 3). The coupling to the total angular momentum ~J is determined byJJ-coupling rather than LS-coupling because mercury belongs to the heaviernuclei.

The lowest excited level is the 3P level, i.e. L = 1 resulting in a J = L - S, ..., L + S = 0,1,2 . According to Hund’s rules for levels less than half-filled theenergy is minimized so that the 3P0 level is the lowest. Higher levels than

3Pdo not play a role in our experiment since the mean free path of the electronsis too short to gather a sufficient amount of kinetic energy for an excitation(see also section 4.7).

In order to calculate the probability of a transition between two atomic energylevels the Schroedinger equation coupled to the resonant light field is solved

5

in linear pertubation theory. It turns out that the term

(ϑij) =∫

dV ϕ∗

i ezϕj (2)

called dipole matrix element, necessarily must be unequal zero. This con-dition implies the following optical selection rules, valid for JJ-coupling:∆J = 0,±1 where J = 0 → J = 0 is forbidden; and ∆j = 0,±1 for thefirst electron, ∆j = 0 for all other electrons. The former rule leads to theconclusion that only the transition 3P1 →

1 S0 is optically allowed corre-sponding to the intensive 253,7nm line whereas the 3P2 and

3P0 states aremetastable and are de-excited by collisions for which the constraints of theoptical selection rules are not valid.

Figure 3: Termscheme of Hg

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2.4 Kinetic gas theory

In kinetic gas theory atoms are considered as hard spheres, i.e. they onlyinteract if their distance becomes smaller than the sum of their gas-kineticradii. Therefore the area around an atom in which another atom will bescattered, defined as the cross section σ, is given by

σ = π(r1 + r2)2 (3)

For an ensemble of such atoms, only interacting by collisions, the ideal gaslaw

p = nkBT (4)

holds with n being the particle density. In a beam of N0 atoms flying througha gas a number

N = N0e−nσx (5)

will be scattered along a distance x. By definition and using equation (5)one finds for the mean free path

Λ ≡1

N0

∫

∞

0x ·

∣

∣

∣

∣

∣

dN

dx

∣

∣

∣

∣

∣

dx = nσ ·∫

∞

0xe−nσxdx =

1

nσ(6)

The mean collision time, that is the time between the collision of two atoms,is defined as

τ =Λ

v(7)

where v is the mean velocity.

2.5 Collisions

Electrons in the vacuum tube can interact with mercury atoms either byelastic or inelastic collisions. Since the electron mass is much lower thanthe mass of a mercury atom electrons hardly lose energy in elastic collisions(∆E ∝ 4 me

mHg) but only change their direction. Therefore the processes we

are interested in must be caused by inelastic collisions, in which a fraction ofthe electron energy is converted into internal, in our case excitational energyof the atom.

2.6 Two-phase system

In the Franck-Hertz tube a liquid mercury drop partially evaporates with in-creasing temperature. This two-phase system of liquid and vapor is described

7

by the Clausius-Clapeyron equation

dp

dT=

λ

(Vv − Vl)T(8)

where p is pressure, T temperature, λ the vaporisation energy and Vv and Vlthe volumina of the vapor and liquid phase respectively. Further processingof this formula and inserting values for the mercury atom leads to

lg p = 10, 55−3333

T− 0, 86 · lg T (9)

where T is given in Kelvin and p is given in Torr (1 Torr = 133,33 Pa).

2.7 Photomultiplier

A Photomultiplier is a sensitive device which converts light into a measur-able electric current. Incident radiation impinges on a photocathode builtof photosensitive material (mainly semiconductors) causing electrons to beemitted due to the photoelectric effect with an efficiency of up to 30%. Bymeans of electric fields the electrons are accelerated and focused on the firstdynode where their energy is transferred to the dynode material. This way3 to 10 secondary electrons per incident electron are released which are thenaccelerated towards the second dynode. A potential ladder of 10 to 14 dyn-odes leads to a total amplification of the current by a factor of about 107.The resulting pulse signal at the anode is ideally proportional in amplitudeto the energy of the corresponding incident photon unless the photomulti-plier is saturated. The schematic structure of a photomultiplier is given infigure 4 on page 8.

Figure 4: General structure of a photomultiplier

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2.8 Interference-filter

Interference filters are based on the concept of a Fabry-Perot interferome-ter which consists of two plane parallel transparent elements separated bya distance d. Its basic principle is shown in Figure 5. Provided that anincident plane wave of wavelength λ is not inclined there will be constructiveinterference of incident and reflected waves for λ = 2 · nd

mwhere n is the

refractive index of the material in the slit and m ∈ N. All other wavelengthsare suppressed so that the setup works as a wavelength filter. In our experi-ment a filter with an approximately Gaussian-shaped transmittance functioncentered around 254,5nm and with a FWHM of 20nm is in use.

Figure 5: Principle of a Fabry-Perot interferometer

3 Setup of the experiment

Figure 6 indicates the setup of the Franck-Hertz experiment. The centralelement of the experiment is the Franck-Hertz tube (see section 2.1) placedin a heated oven. The temperature can be measured by a digital thermome-ter. The cathode is heated by an alternating voltage of 6,3 V. The maximumaccelerating voltage UB

max can be adjusted from 0 to 50 V. Throughout theexperiment we set the value to 40 V, which turned out to be a reasonablevalue. We achieve a linear increase of UB, which is connected to the X-inputof the plotter, by loading a capacity C with a constant current. Opening and

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closing the included switch S1 starts and stops the measurement. After beingamplified the anode current controls the Y-deviation of the analog plotter.

Furthermore there is a UV-transparent window in one side of the oven. Aninterference-filter selects the 254nm transition of mercury followed by a pho-tomultiplier which converts the incident photons into a measureable current.We set the operational voltage of the photomultiplier to 300 V. After itsamplification this photocurrent is connected to the Y-input of the plotter.Besides we can include a RC-device into the circuit in order to plot thedifferentiated photocurve.

Figure 6: Setup of the experiment

4 Implementation and analysis

4.1 Proceeding

We plotted the Franck-Hertz curves for four different temperatures

T = 150◦C, 159◦C, 171◦C, 184◦C

and two different countervoltages

UG = 0,5V, 1V

We assume the error on temperature to be σT = 1◦C and the error on coun-

tervoltage to be σUG= 0, 05V .

10

The photocurve and its derivative were measured for all four temperatureswith a constant countervoltage UG = 0, 5V . At 150

◦C an additional pho-tocurve was taken for UG = 1V . As expected it turned out to be the sameas for UG = 0, 5V for the emission of light not being correlated with thedeacceleration of electrons behind the grid.

Furthermore we inserted a glass plate between the oven and the photomul-tiplier to make sure that we measure UV light indeed. As expected thephotocurrent immediately broke down when shielding the beam.

For each temperature we proceeded in the following way: plot of the Franck-Hertz curves, plot of the photocurve, plot of the differentiated photocurve.Temperature was gradually increased.

4.2 Calibration

For the temperatures T = 150◦C and T = 159◦C a Y-scale of the plotter of0, 2 V

cmwas chosen to get an adequate resolution of the curves. In order to

avoid the curves to become to small we increased the Y-scale to 0, 1 Vcmfor

the two higher temperatures. In both cases an amplifier sensibility of 0, 1µAwas selected. At all temperatures the parameters for the photocurves had tobe changed to 10nA amplification sensibility and a Y-scale of 0, 1 V

cmand for

its derivative to 1nA and to 0, 05 Vcmrespectively.

Throughout the experiment the X-scale of the plotter was 2 Vcm. Although the

X-scale was run in the calibrated mode, the actual scale did not correspondto this adjustment. This can be easily deduced from the fact that all curvesare longer than 20 cm in x direction taking into account a total UB rangeof 40 V. Fortunately we observed the linearly increasing UB on an analogvoltmeter and marked tics with a distance of 10V each on the graphs. Ofcourse this method is not very exact, but averaging over our own calibrationon all eight graphs yields an acceptable result. The measured distances d be-tween two tics can be found in table 6.1. We calculated the arithmetic meand = 5, 6cm and standard deviation σd = 0, 2cm. Then the actual X-scale ccan be calculated by c = 10V

dand its error σc by σc =

10V

d2 · σd.

Thus our final result for the actual X-scale is

c = 1, 80± 0, 06V

cm(10)

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4.3 Features of the Franck-Hertz curves

The plotted Franck-Hertz curves distinctly show the expected sequence ofminima and maxima as mentioned in section 2.1. One can recognize thefollowing characteristics of the curves:

The curves for the higher countervoltage of 1V run below the curves for thecountervoltage of 0,5V. This can be put down to the fact that the electronsneed to have a higher kinetic energy behind the grid to overcome a highercountervoltage. Thus low energetic electrons cannot reach the anode, whichleads to a smaller anode current.

With rising temperature the location of minima and maxima is shifted tohigher voltages. Besides we recognize an offset voltage as the position of thefirst maximum is located at higher voltages than the expected 4,9V. We ex-plain these phenomena by a temperature dependent contact voltage betweenthe electrodes.

The overall amplitude of the Franck-Hertz curves decreases with rising tem-perature. Higher temperatures cause a higher particle density of mercuryatoms, so that the mean free path of the electrons decreases (see equation(6)). Therefore more electrons are scattered between grid and anode. If thescattering angle becomes greater than π

2the electrons are accelerated back-

wards to the grid by the countervoltage and do not contribute to the anodecurrent anymore.

The amplitude of a single maximum increases with higher acceleration volt-age UB, because it follows the expected current voltage characteristic of avacuum tube as depicted in figure 2. Due to statistical fluctuations and thekinetic energy distribution of the electrons the anode current in the minimaremains larger than zero.

4.4 Analysis of the Franck-Hertz curves

We determined the distances x between the minima which provided the mostdistinct features in each Franck-Hertz curve for all sets of parameters. Thesevalues including all derived quantities mentioned in this paragraph can befound in section 6.2.1 and 6.2.2. Due to the limited accuracy in reading outthe figures we assumed an individual error of σx.

According to U = c ·x we arrive at the corresponding voltages. The resulting

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systematic error reads

σU =√

c2 · σ2x + x2 · σ2

c (11)

For each fixed set of parameters we calculate a weighted mean

U =

∑

U/σ2U

∑

1/σ2U

(12)

with a total systematic error

σ′

U=

√

1∑

1/σ2U

(13)

In addition to this we calculated the standard deviation of the voltages σ ′′

U

leading us to the total error on U

σU =√

σ′2

U+ σ′′2

U(14)

The following table contains our results so far:

T [◦C] UG [V] U [V] σU [V]150 0,5 4,90 0,23150 1,0 4,83 0,18159 0,5 4,90 0,15159 1,0 4,86 0,12171 0,5 4,89 0,18171 1,0 4,82 0,16184 0,5 4,72 0,17184 1,0 4,74 0,17

Especially at the highest temperature we observe a significant decrease in U .The other values include the theoretical value of U = 4, 90V .

Averaging all the U similar to equations number (12) and (13) we arrive atour final result for the excitation voltage Uex:

Uex = (4, 83± 0, 06)V (15)

Unfortunately the theoretical value lies slightly outside the error boundaries,which might be estimated too optimistically when taking into account theinaccuracy of our calibration.

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The corresponding wavelength of the optical transition is given by

λ =h · c

e · Uex

(16)

with an error of

σλ =h · c

e · U 2ex

σUex(17)

yielding λ = (257 ± 3)nm. Again this does not quite match the theoreticalvalue of 253,7nm.

4.5 Features of the photocurrent curves

The photocurrent curves resemble an exponential function revealing equidis-tant kinks in the slope. These can be recognized more easily in the differen-tiated curves plotted on the same sheet. The differentiated curves look likea heavily disturbed step function. Both the photocurve and its derivativedecrease in amplitude with rising temperature, because the mean collisiontime between mercury atoms diminishes. So de-excitations preferentiallytake place by collisions rather than by optical transitions by virtue of theirrelatively long lifetimes (see also 4.7).

In order to explain the shape of the curves one has to consider two aspects.The photocurrent increases with acceleration voltage since the number ofelectrons and subsequently the number of excitations in the tube goes up.Moreover the kinks or steps respectively originate in the increasing numberof excitations per single electron on the way from cathode to grid, e.g. ifelectron gather enough energy to excite two mercury atoms, twice the num-ber of photons can be produced and so on. The voltage distance between thesteps is again equal to the excitation voltage of the observed transition.

When switching off the light in the laboratory we observed thin layers ofbluish light parallel to the grid in the Franck-Hertz tube. According to ourexplanations so far the number of layers as well as the intensity of the bluelight increased with rising acceleration voltage.

4.6 Analysis of the photocurrent curves

Analysing the photocurrent curves we used our own calibration (see sec-tion 4.2). As the steps in the differentiated photocurrent curve are not ver-tical we decided to measure the distances between the middles of the risingslopes. We only used well defined steps without artefacts and too heavy noise

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pertubations. The results can be found in table 6.3 on page 22. Due to thenumerous sources of inaccuracy we estimate a systematic error on the dis-tance measurements of σx = 0, 2cm. Again we calculate the correspondingvoltage U = c·x and its error σU according to equation (11). Using equations(12), (13) and (14) we arrive at

Uex = (5, 0± 0, 2)V (18)

Keeping in mind the limited accuracy this result matches the theoretical valueand agrees with the outcome of the analysis of the Franck-Hertz curves.

4.7 Calculation of mean free path and collision time

We will now calculate the mean free path of an electron with a kinetic energyof 5 eV at a temperature of 171◦C ≡ 444, 15K . According to equation (9)the pressure p in the tube is

p = 1010,55−3333

T−0,85·lg T

≈ 832, 16Pa (19)

The cross section for the excitation of the triplet P-levels of mercury can beread out from Figure 7 on page 16: σ(3P0) = 1πa

2, σ(3P1) = 2, 5πa2 and

σ(3P2) = 0 with a ≡ Bohr’s radius yielding

σtot = 3, 5πa2≈ 3, 092 · 10−20m2 (20)

Making use of the ideal gas law p = nkBT we arrive at the mean free path

Λ =1

n · σtot=

kBT

σtotp≈ 238, 1µm (21)

So the 5 eV electron will excite a 6P-triplet level by collision and as a conse-quence lose its kinetic energy before it is able to gather enough energy for anexcitation of a higher level. Therefore the assumption is justified that higherenergy levels than the 63P -level can be neglected.

In order to calculate the time between the collision of two mercury atoms werefer to the gas-kinetic cross section of mercury atoms given by

σHg→Hg = π · (dHg

2+

dHg

2)2 = πd2

Hg ≈ 6, 08 · 10−19m2 (22)

where dHg = 0, 44nm, the gas-kinetic diameter, was given in the scriptum.

15

Considering the Maxwell-Boltzmann distribution the mean velocity of mer-cury atoms in the gas at temperature T is

v =

√

√

√

√

8kBT

πmHg

≈ 216, 5m

s(23)

where mHg = 200, 59u with u being the atomic mass unit. Finally thecollision time is

τ =Λ

v=

1

v · n · σHg→Hg

=kB · T

v · p · σHg→Hg

≈ 55, 9ns (24)

Regarding the fact that the lifetime of the optical transition 3P1 →1 S0 (117

ns) is more than twice as great as the determined time between two collisionsτ , a lot of atoms will most likely deexcite by collision than by emission of aphoton.

Figure 7: Total cross section for the excitation by electron impact.Curve 1: 61S0 → 63P0 excitation. Curve 2: 6

1S0 → 63P1 excitation.Curve 3: 61S0 → 63P2 excitation. Curve 4: 6

1S0 → 61P1 excitation.

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5 Summary

Our results for the excitation voltage of the 3P level of mercury are in rel-atively good agreement with the expected value within the framework ofmeasurement accuracy. The analysis of the Franck-Hertz and photocurrentcurves are in principle both suitable for precise measurement, but in our casewere limited because of poor calibration. Therefore it would have been ap-propriate to put more emphasis on determining the features of the plotter.Besides the quality of the differentiated photocurrent curves suffered fromthe heavy noise (also in a literal sense), which we were not able to overcome.

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6 Appendix

6.1 Table of data - calibration

number d [cm] number d [cm]1 5,3 17 5,42 5,6 18 5,73 5,8 19 5,54 5,5 20 5,55 5,4 21 5,66 5,6 22 5,57 5,9 23 5,88 5,4 24 5,49 5,6 25 5,410 5,5 26 5,811 5,8 27 5,712 5,3 28 5,413 5,4 29 5,314 5,8 30 5,815 5,8 31 5,916 5,3 32 5,3

Table 1: Distance d between 10V tics

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6.2 Tables of data - Franck-Hertz curves

6.2.1 Databasis

In the column ’minima’ the minima are indicated whose distance is given inthe corresponding row.The remark ’np’ indicates that no accurate measurement could be performed.

T [◦C] UG [V] minima x [cm] σx [cm] U [V] σU [V]1 150 0,50 1 - 2 2,50 0,20 4,50 0,392 150 0,50 2 - 3 2,70 0,15 4,86 0,313 150 0,50 3 - 4 2,70 0,10 4,86 0,244 150 0,50 4 - 5 2,80 0,10 5,04 0,255 150 0,50 5 - 6 2,70 0,10 4,86 0,246 150 0,50 6 - 7 2,80 0,10 5,04 0,25

Table 2: Data at T = 150◦C and UG = 0, 50V

T [◦C] UG [V] minima x [cm] σx [cm] U [V] σU [V]7 150 1,00 1 - 2 2,50 0,20 4,50 0,398 150 1,00 2 - 3 2,70 0,15 4,86 0,319 150 1,00 3 - 4 2,70 0,10 4,86 0,2410 150 1,00 4 - 5 2,70 0,10 4,86 0,2411 150 1,00 5 - 6 2,70 0,10 4,86 0,2412 150 1,00 6 - 7 2,70 0,10 4,86 0,24


T [◦C] UG [V] minima x [cm] σx [cm] U [V] σU [V]13 159 0,50 1 - 2 np np np np14 159 0,50 2 - 3 2,70 0,20 4,86 0,3915 159 0,50 3 - 4 2,70 0,15 4,86 0,3116 159 0,50 4 - 5 2,70 0,10 4,86 0,2417 159 0,50 5 - 6 2,70 0,10 4,86 0,2418 159 0,50 6 - 7 2,80 0,10 5,04 0,25


19







T [◦C] UG [V] minima x [cm] σx [cm] U [V] σU [V]37 184 0,50 1 - 2 np np np np38 184 0,50 2 - 3 np np np np39 184 0,50 3 - 4 2,60 0,20 4,68 0,3940 184 0,50 4 - 5 2,70 0,15 4,86 0,3141 184 0,50 5 - 6 2,60 0,10 4,68 0,2442 184 0,50 6 - 7 2,60 0,10 4,68 0,24


20

T [◦C] UG [V] minima x [cm] σx [cm] U [V] σU [V]43 184 1,00 1 - 2 np np np np44 184 1,00 2 - 3 np np np np45 184 1,00 3 - 4 2,60 0,20 4,68 0,3946 184 1,00 4 - 5 2,60 0,15 4,68 0,3147 184 1,00 5 - 6 2,70 0,10 4,86 0,2448 184 1,00 6 - 7 2,60 0,10 4,68 0,24

Table 9: Data at T = 184◦C and UG = 1, 00

6.2.2 Interim results

basis table U [V] σ′

U[V] σ′′

UσU

1 4,90 0,11 0,20 0,232 4,83 0,11 0,15 0,183 4,90 0,12 0,08 0,154 4,86 0,12 0,00 0,125 4,89 0,12 0,13 0,186 4,82 0,12 0,10 0,167 4,72 0,14 0,09 0,178 4,74 0,14 0,09 0,17

Table 10: Interim results calculated on the basis of the tables in section 6.2.1as described in section 4.4.

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6.3 Table of data - photocurrent curves

T [◦C] x [cm] σx [cm] U [V] σU [V]1 150 2,9 0,2 5,22 0,402 150 2,8 0,2 5,04 0,403 159 2,8 0,2 5,04 0,404 159 2,8 0,2 5,04 0,405 159 2,7 0,2 4,86 0,396 159 2,9 0,2 5,22 0,407 171 2,7 0,2 4,86 0,398 171 2,8 0,2 5,04 0,409 171 2,7 0,2 4,86 0,3910 184 2,7 0,2 4,86 0,3911 184 2,7 0,2 4,86 0,39

Table 11: Measured distances between two steps in the differentiated pho-tocurrent curves as described in section 4.6.

22

6.4 Legend concerning the original plots

• Franck-Hertz curves

– Sheet 1: T = 150◦C; black line ≡ (UG = 0,5V);green line ≡ (UG = 1V)




• Photocurrent curves

– Sheet 5: T = 150◦C; black line ≡ photocurrent curve;thick black line ≡ differentiated photocurrent curve




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References

[1] Haken, Wolf: Atom- und Quantenphysik, edition 8, Springer-Verlag(2004)

[2] Demtroeder: Experimentalphysik 2, edition 1, Springer-Verlag (1995)

[3] Demtroeder: Experimentalphysik 3, edition 2, Springer-Verlag (2000)

[4] Advanced Laboratory Scriptum, University Bonn (2005)

This report contains several figures which are taken from the following sources:Figure 1, 2 and 4 were taken from [3].Figure 3 was taken from [1].Figure 5 was taken from [2].Figure 6 and 7 were taken from [4].

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