1. Franck and Hertz Experiment By Professor Imran Ahmad

2. What was the Experiment of Franck and Hertz? Franck and Hertz had designed a vacuum tube for studying energetic electrons that flew through a thin vapor of mercury atoms. They discovered that, when an electron collided with a mercury atom, it could lose only a specific quantity (4.9 electron volts) of its kinetic energy before flying away.

3. What was the experiment of Franck and Hertz? Photograph of a vacuum tube used for the Franck–Hertz experiment in instructional laboratories. There is a droplet of mercury inside the tube, although it is not visible in the photograph. C - cathode assembly; the cathode itself is hot, and glows orange. It emits electrons which pass through the metal mesh grid (G) and are collected as an electric current by the anode (A)

4. What was the main purpose of Franck-Hertz Experiment? The aim of the Frank-Hertz Experiment procedure is to demonstrate the concept of quantisation of the energy levels in accordance with the Bohr's model of an atom.

5. Based on the following experimental setup, James Franck and Gustav Hertz provided an amazing experimental confirmation for the energy quantization of atoms in 1914. In a mercury vapor-filled light bulb with low pressures, the grid G is used to accelerate electrons that are emitted from a heated cathode to the energy Ekin = eU. The collecting anode A, which is maintained at a lower voltage UA = U-∆U, can only be reached by electrons whose energy after passing the grid G is at least ede∆U.

6. Structure of Franck-Hertz Experiment

7. Franck-Hertz Experiment

8. The electrons suffer elastic and inelastic collisions with the Hg atoms. In inelastic collisions, e − (E kin )+H g → H g ∗ (E a )+e − (E kin − E a ) the electrons excite the Hg atoms and transfer the amount ∆E kin = E kin − E a of their kinetic energy to the excitation energy Ea of the atom. Because of this loss of energy the electrons cannot overcome the bias voltage −∆U and therefore cannot reach the detector.

9. Franck-Hertz Experiment During elastic collisions the electron can at most transfer the fraction 4m e /mH g ≈ 10 −5 of its kinetic energy. At sufficiently low pressures each electron suffers only a few elastic collisions and the total energy loss due to elastic collisions is then completely negligible. However, elastic collisions may result in large angular changes of the electron’s flight direction and the electrons may therefore hit the walls of the tube before they reach the anode. Without inelastic collisions the electron current would follow the dashed curve in which resembles the electron current in a diode tube. The further maxima and minima in the actually measured current I(U A ) are due to the fact that at sufficiently large voltages U the electron can regain,after n inelastic collisions, the minimum required kinetic energy e∆Z during its flight path to the grid G but has not enough energy for the (n +1)th inelastic collision

10. Franck-Hertz Experiment The separation between subsequent maxima corresponds to the excitation energy Ea = 4.9 eV of H g atoms. The exact form of the curve I(U) is determined by The energy dependence of the excitation probability The energy distribution of the electrons emitted from the hot cathode.

11. Franck-Hertz Experiment With the improved experimental setup of the energy resolution could be substantially improved. Here, two grids are used and the acceleration of the electrons is essentially restricted to the short flight path between K and G 1, while the small adjustable voltage U 2 between G 2 and G 1 does not change the electron energy much. The excitation probability is then nearly the same for all points between G 1 and G 2. With such an improved apparatus the finer details of the excitation function could be resolved, which correspond to different excited states of the H g atoms.

12. Franck-Hertz Experiment

14. The excited Hg ∗ atoms release their excitation energy by emission of light Hg ∗ → Hg+hν. Measuring this fluorescence light through a monochromator shows that the emitted spectral lines have wavelengths λk, which exactly correspond to the measured absorption lines of Hg vapor. Time-resolved measurements of this fluorescence prove that the excited atomic levels E i are not stable. They decay within a very short time (typically ≈ 10−8 s) into lower states E k, where ∆E = E k − E i = hν ik = hc/λ ik

15. Franck-Hertz Experiment Only the lowest atomic states (called the ground states) are stable. Their lifetimes are infinitely long (if not excited by collisions or absorption of photons). The wavelength λik of the emission spectrum measured through a spectrograph allow a much higher accuracy in the determination of energy levels than those obtained from the electron impact measurements

16. Experimental Results The experimental results of the electron impact excitation prove that atoms can acquire energy only in discrete energy quanta ∆E. Their magnitude depend on the specific atom and its level structure.