Franck-Hertz Experiment
1 Introduction Planck (1900) put forward the idea of quantization while solving a long standing problem of the black body radiation. He proposed that the exchange of the energy between the radiation and the matter is discrete rather than continuous. This hypothesis fueled to look for a modification in the understandings of classical physics which only deals with the continuous exchange of energy. In 1905, Einstein solved the photoelectric effect problem assuming the quantization of the light. Inspired from the success of Planck’s hypothesis and Einstein’s theory, Bohr proposed the quantization theory in describing the spectrum of hydrogen atom. According to Bohr’s assumptions, the electron in an atom revolves around the nucleus in a circular orbit under the influence of the electrostatic attraction of the nucleus placed at the centre of the orbit. Also, the electron is allowed to move in a certain set of orbits called as stationary states with discrete energy values. While moving in these orbits the electron does not radiate its energy. In these orbits the angular momentum of the electron is quantized and can take values equal to the integral multiple of h/2π, where h is the Planck constant. Each of such states of atom having a fixed energy value are called as atomic energy level. The transitions from one energy level to another can happen only if a photon of the energy equal to the difference of energies between the two energy levels is absorbed or emitted. For instance a transition between two discrete atomic energy levels Ea and Eb is associated with emission or absorption of a photon of frequency ν=(Ea-
Eb)/h. Bohr’s theory successfully explained the observed spectrum of the hydrogen atom and established the belief that the transfer of energy to the electrons in an atom by any mechanism should always be in discrete amounts. However, this theory required endorsements from the experiments other than the spectroscopy of Hydrogen. One such mechanism of energy transfer is through the inelastic scattering of low- energy electrons which was explored through series of experiments on the mercury vapor by James Franck and Gustav Hertz in 1914. The results of this experiment are indictment that the atoms can absorb energy only in discrete amount, no matter how the energy is supplied to the atoms. As per James Franck confessions (Gerald Holton, Americal Journal of Physics, vol. 29 p.805 (1961)) Franck and Hertz were not aware of Bohr’s theory while performing their experiment. The early days of spectroscopy and the close observation of spectral lines was motivation for the setup of this peculiar experiment. Their aim was to find the borderline between the elastic collision and inelastic collision with an expectation of only one emission line in the spectrum and to their surprise, they could reach to their expectation, and the emission line 4.89 eV for mercury which corresponds to the 2536 Å ultra- violet line. 2 Theoretical Understanding Thermionic emission is a useful technique to get a source of the electrons. The cathode plate while heated emits electrons with the very small kinetic energy. These electrons can be pushed by a grid (G1) kept on a slightly positive potential relative to the cathode plate while passing through the glass tube filled with an inert gas (See Fig. 1). In the original experimental set up by Franck and Hertz mercury vapours were kept inside the glass tube. However, in the present experimental set up the tube is filled with the argon gas. Usually the monoatomic gases like Argon, Mercury, Neon etc., are filled in the chamber in order to prevent complications involving molecular transitions. Few details about argon (Ref.: NIST Basic atomic spectroscopy data) are given below:
Atomic number Z=18
Electron configuration= [Ne]3s2 3p6
1st Ionization energy=15.75 eV
2nd Ionization energy=27.62 eV
3rd Ionization energy=40.74 eV
Accelerating potential is applied by introducing another grid (G2) which is kept positive relative to the cathode and anode plates. This grid G2 acts as a filter for higher energy electrons to pass through it. During the motion of electrons from the cathode to anode plate there is a possibility of collision with the gas atoms inside the tube. This collision may be elastic or inelastic in nature depending upon the energy of the electrons. If the electron collides with the argon gas elastically the energy loss of the electron will be negligible (me << MAr) and electron would pass through the anode without affecting the Argon atom. In the case of argon this elastic collision happens for the electrons with energy less than 11.83 eV. If the electron acquires energy nearly equal to 11.83 eV, the collision is inelastic and a part of the energy of the electron may be available to excite the argon atom. The energy level diagram of argon atom is shown in fig. 2. The electron after collision slows down and unable to reach at the anode depending upon the potential difference between the grid G2 and anode. This results a drop in the current while increasing the potential between the cathode and grid G 2. Let us consider that the electron is accelerated due to the potential difference V between the cathode and grid G2 and V-∆V be the potential difference between the grid G2 and the anode. In that case the electron needs minimum e∆V energy to reach at the anode and contribute to the current in the circuit. The Franck-Hertz experiment demonstrates that the current in the circuit increase as we increase the potential V till a cutoff value Vc1 is reached with a maximum current output.
However, above Vc1, the current declines and reaches to a minimum at Vc2. This trend follows the pattern of periodic maximum and minimum currents in the circuit (Fig. 4). Classical physics has no explanation of this behaviour. Fig. 1 A circuit diagram for the Franck-Hertz experiment. (Diagram is taken from the user Manual for FH3001) This maxima and minima of the output current can be explained by the inelastic collision of electrons with the argon atoms. Only those electrons with a critical value Vc1 hitting the argon atoms, transfer their energy and excite the argon atoms. During the process of inelastic collision they loss their kinetic energy, and unable to reach the anode resulting a significant drop in the current output after Vc1. At Vc2 maximum number of these energetic electrons loose their energy and a minimum in current can be observed. Others electrons still have sufficient energy to pass through the barrier voltage between the anode and grid G2 and contribute to the net current. It is interesting to see that both the minimum and maximum values of the current grow larger with increasing accelerating voltage in a similar fashion of a diode or a tetrode. Further increasing the voltage again raises the energy of the electrons. There is a possibility that those electrons who retarded after exciting the argon atom gain sufficient energy between two collision and excite several argon atoms. Another possibility is that the electrons starting from the cathode gain sufficient energy to excite more than one atom. Therefore, the peak of the next maximum is higher than the preceding one. A sharp downfall of the current after the second peak can be attributed to those electrons that suffered two inelastic collisions with two argon atoms, losing all their kinetic energy and so on. Fig. 2 Energy level diagram for Argon atom. 3 Objectives To verify the existence of discrete atomic energy levels of Argon atom and determine the minimum excitation energy of argon. 4 Experimental setup: The Franck-Hertz experiment setup model no. FH 3001 from SES Instruments Pvt. Ltd. is used. The setup as depicted in the user manual for FH 3001 is shown in Fig. 3. The circuit diagram for the setup is shown in Fig. 2. The FH3001 setup consists of
Argon filled tetrode;
Filament Power Supply: 2.6-3.4V continuous variable;
Grids Power Supplies: VG1K: 1.3-5V continuous variable, VG2A 1.3-12 V continuous
variable, VG2K: 0-95 V continuously variable ;
Sawtooth waveform for CRO display
Multirange Digital Ammeter (Range multipliers: 10-7, 10-8, 10-9 ) Apart from the FH 3001 model, a 30 MHz Cathode Ray Oscilloscope from Scientech 801 is also provided to analyze the current vs voltage graph in the automatic mode. The Oscilloscope in this experiment is required to keep in XY mode. In this mode the setting of the oscilloscope is such that the voltage measured on channel one is displayed on the x axis and and voltage measured on the channel two is on Y axis. Fig. 3 Franck-Hertz experiment setup model no. FH 3001. (Picture is taken from the user manual of FH 3001) 5 Experimental Procedure 5.1 Manual Mode
Ensure that the Electrical power is 220V ± 10%, 50 Hz.
Before the power is switched ‘ON’ make sure all the control knobs are at their minimum position and Current Multiplier knob at 10-7 position.
Switch on the Manual-Auto Switch to Manual, and check that the Scanning Voltage Knob is at its minimum position.
Turn the Voltage Display selector to VG1K and adjust the VG1K Knob until voltmeter reads 1.5 V.
Turn the voltage Display selector to VG2A and adjust the VG2A Knob until the voltmeter read 7.5 V.
Before proceeding to the next step check that the initial parameters are Filament Voltage: 2.6V (minimum position) VG1K : 1.5 V VG2A: 7.5V VG2K : 0V Current Amplifier: 10-7 These are suggested values for the experiment. The experiment can be done with other values also. Rotate VG2K knob and observe the variation of plate current with the increase of VG2K . The current reading should show maxima and minima periodically. The magnitude of maxima could be adjusted suitably by adjusting the filament voltage and the value of current multiplier.
Now take the systematic readings, VG2K vs Plate Current. For better resolution and
observation of the maxima / minima VG2K is varied from 0-80 V in the increments of 0.1 V or 0.01 V. Increments of 0.1 will be used for the data set away from the peak or the dip. The interval 0.01V may chosen to finer the observation near maxima or minima.
Plot the graph with output current on Y- axis and Accelerating Voltage VG2K at X-axis. 5.2 Auto Mode
Turn the Manual-Auto switch to ‘Auto’, connect the instruments Y, G, X sockets to Y, G, X of Oscilloscope. Put the Scanning Range switch of Oscilloscope to X-Y mode/external ‘X’.
Switch on the power oscilloscope, adjust the Y and X shift to make the scan base line on the bottom of screen. Rotate The Scanning Knob of the instrument and observe the wave form on the Oscilloscope Screen. Adjust the Y-gain and X-gain of oscilloscope to make wave form clear and Y amplitude moderate.
Rotate the scanning potentiometer clockwise to end. Then the maximum scan voltage is 85V.
Measure the horizontal distance between the peaks. The distance of two consecutive peaks (no of grids) and multiply it by V/ grid factor (X-gain) of oscilloscope. This would give the value of argon atom’s first excitation potential in eV. 6 Observations: 6.1 Manual Mode: Accelerating voltage versus Current Least count of Voltmeter = 0.1 V Least count of Ammeter=10-9 A VG1K : 1.5 V VG2A: 7.5 V
S. No. Accelerating Voltage (VG2K) Current (IA)
1 --- --
2 --- --
3 -- --
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Fig. 4 The current vs accelerating voltage VG2K observed from the Franck-Hertz experiment for the argon atoms. 6.2 Auto Mode: Accelerating voltage versus Current from CRO display
Fig. 5 Display of the CRO screen arranged for the Franck-Hertz experiment. 7 Calculations
VG2K at maximum current (Volts) Difference from the preceding maximum (Volts)
11 0
22 11
32 10
43 11
54 11
66 12
Average difference between the two maxima = 11 V. The maximum possible error in the measurement is the least count of the voltmeter i. e.; 0.1 V.
However, while performing the above measurement, VG2K is changed by an increment of 1 V. The measurement of differences double the maximum possible error in the calculated value. Please see fig. 6 where averaged difference is compared with the actual data set with error bars.
Fig. 6 The peak value of VG2K is plotted against the order of the maxima. 8 Results and Discussion:
As seen from the curve between the current and VG2K graph the electrons can excite the argon atoms only if they are accelerated by a specific value of the voltage or its integer multiples. This verifies the discrete atomic energy levels of the argon atoms. A significant decrease in electron (collector) current is noticed every time the potential on grid 2 is increased by approximately (11 ± 2) eV, thereby indicating that the energy is transformed from the beam in quanta of (11 ± 2) eV only. The average value of spacing between the peaks is 11 eV compared to the first excited state of the argon atom 11.83 eV observed from the spectroscopy evidences. 9 Precautions:
Before taking the systematic readings, gradually increase the value of VG2K to a maximum. Adjust the filament voltage if required such that maximum readings are about 10.00 on x 10-8 range. This will ensure that all the readings could be taken in the same range.
During the experiment (manual), when the voltage is over 60V, please pay attention to the output current indicator, IF the ammeter readings increases suddenly, decrease the voltage at once to avoid the damage of the tube.
Whenever the filament voltage is changed, please allow 2/3 minutes for its stabilization.
When the Franck-Hertz Tube is already in the socket, please make sure the following before the power is switched ‘ON’ or ‘OFF’, to avoid damage to the tube.
1. Manual-Auto switch is on Manual and Scanning and Filament Voltage knob at its minimum position (rotate it anticlockwise) and current multiplier knob at 10-7.
2. VG1K, VG2A, and VG2K all three knobs are at their minimum position.