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Franck Hertz Experiment Franck Hertz experiment By : Muzamil Shah Preview of Things to Come History Theory Setup Results Conclusions History In 1914, by James Franck and Gustav Ludwig Hertz One year after Bohr’s theory of quantized energy states Nobel Prize in 1925: “for their discovery of the laws governing the impact of an electron upon an atom” Theory Inelastic scattering of electrons Confirms Bohr’s Energy quantization Electrons ejected from heated cathode at zero potential are drawn towards the positive grid G. Those passing through hole in grid can reach plate P and cause current in circuit if they have sufficient kinetic energy to overcome the retarding Potential between G and P Tube contains low pressure gas of stuff! If incoming electron does not have enough energy to transfer =E2-E1 then Elastic scattering, if electron has at least KE= then inelastic scattering and the electron does not make it to the plate P Loss of current Theory Current decreases because many Electrons lose energy due to inelastic Scattering with the Hg atom in tube And therefore can not overcome the Small retarding potential between G P The regular spacing of the peaks Indicates that ONLY a certain quantity Of energy can be lost to the Hg atoms =4.9 eV. This interpretation can be confirmed by Observation of radiation of photon energy E=hf=4.9 eV emitted by Hg atom when V0 > 4.9V Theory For n inelastic collisions the energy gained by the electrons is Where Ea is the lowest excitation energy and is additional energy The spacing between two minima in a Franck-Hertz curve is given by The mean free path of the electrons can be written as Theory Theoretically mean free path is given by where is the cross section for inelastic collisions In the temperature range from 300 to 500 K the mercury pressure p is given as Setup of Frank-Hertz Experiment Experimental data Temp 145 C n 1234 Ea (eV) 4.4 4.8 5.2 6 Temp 150 C n12345 Ea (eV) 4.8 5.2 5.6 5.6 6 Temp 155 C n12345 Ea (eV) 4.4 4.8 5.2 5.6 6 Temp 160 C n123456 Ea (eV) 4 4.8 5.2 5.6 5.2 6 Temp 165 C n 1234567 Ea (eV) 4.8 5.2 5.2 5.6 5.2 5.6 6 Temp 170 n 12 34567 Ea (eV) 4.4 4.8 5.2 5.2 5.6 5.6 6 Experimental data T (K) Ea (eV) Lambda Lambda Slope (eV) (micro (micro meter) meter) Theoretical Experimenta l 145 4.20 333.33 243.59 0.52 150 4.74 206.75 201.32 0.28 155 4.20 333.33 167.15 0.40 160 4.14 279.00 139.39 0.33 165 4.41 190.48 116.74 0.24 170 4.88 71.72 98.17 0.10 Result of Frank-Hertz Experiment 80 80 70 70 T=150 C T=145 C 60 60 50 50 40 40 30 30 Anode current (nA) 20 Anode current (nA) 20 10 10 0 0 -10 -10 0 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 80 90 Accelerating Potential (V) Accelerating Potential (V) Result of Frank-Hertz Experiment 70 80 70 60 T=155 C T=160 C 60 50 50 40 40 30 30 20 Anode current(nA) 20 Anode current (nA) 10 10 0 0 -10 -10 0 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 80 90 Accelerating Potential (V) Accelerating Potential (V) Result of Frank-Hertz Experiment 80 80 70 70 T=165 C 60 T=170 C 60 50 50 40 40 30 30 Anode current (nA) Anode current (nA) 20 20 10 10 0 0 -10 -10 0 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 80 90 Accelerating Potential (V) Accelerating Potential (V) Spacing ∆E vs. n 6 6 y = 0.4*x + 4 5.8 y = 0.28*x + 4.6 T=145 5.5 C T=150 5.6 5.4 5 5.2 dE (eV) dE (eV) 5 4.5 X: 0.5017 X: 0.5084 4.8 Y: 4.74 Y: 4.203 4.6 4 4.4 3.5 4.2 0 0.5 1 1.5 2 2.5 3 3.5 4 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 n (number of collision) N (number of minimum n) 6 7 5.8 y = 0.4*x + 4 y = 0.33*x + 4 6.5 5.6 T=155 C T=160 C 5.4 6 5.2 5.5 5 dE (eV) 4.8 dE (eV) 5 4.6 4.5 4.4 X: 0.5017 Y: 4.201 4.2 4 X: 0.5151 Y: 4.144 4 0 1 2 3 4 5 6 N (number of minimum n) 3.5 0 1 2 3 4 5 6 7 N (number of minimum n) Spacing ∆E vs. n 7 7 y = 0.24*x + 4.3 6.5 y = 0.1*x + 4.8 T=165 C 6.5 T=170 C 6 6 dE (eV) 5.5 dE (eV) 5.5 5 X: 0.5017 5 X: 0.5084 Y: 4.884 4.5 Y: 4.409 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 9 10 N (number of minimum n) N (number of minimum n) Lambda vs. T -4 -4 x 10 x 10 2.6 original data original data fit data 2.4 fit data 2.2 3 2 1.8 2 1.6 lambda (m) lamda (m) 1.4 1.2 1 1 0.8 415 420 425 430 435 440 445 0 Temperature (K) 145 150 155 160 165 170 Temperature (C) Theoretical data Experimental data CONCLUSIONS: •Electrons with certain specific energies were not passing through the tube. If the electrons had energies: < 4.9 eV they bounced off the mercury atoms with no loss of energy and continued to the anode = 4.9 eV they collided with mercury atoms and transferred all of their energy to the atom and did not reach the anode (causing the current to drop) > 4.9 eV that collided with atoms gave up 4.9 eV of energy, but sill have some energy left to travel to the anode Thanks.
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