1RR August 2000 SS December 2001 Physics 342 Laboratory Discrete Electron States in an Atom: The Franck-Hertz Experiment Objective: To measure the first excitation potential and the ionization potential of mercury atoms and to show that the energies of bound electrons are quantized. References: 1. J. Franck and G. Hertz, Verhand Deut. Physik Ges. 16 ,10 (1914). 2. A.C. Melissinos, Experiments in Modern Physics, Academic Press, New York, 1966, pgs. 8-17. Apparatus: Franck-Hertz tube, furnace, Kiethley Model 485 picoammeter, Wavetek Model DM2 digital voltmeter (optional), CASSY interface, 10 KΩ potentiometer, a.c. power supply for the furnace (Variac), two 1.5 V batteries, 0-100V d.c. power supply to accelerate electrons, 0-10 V d.c. Lambda power supply for heating the filament, Fluke Model 51 digital thermometer. Introduction An electron bound in an atom does not behave like a classical mechanical system, which can absorb arbitrary amounts of energy. Instead, as suggested by Bohr in 1913, an electron in an atom can exist only in definite discrete stationary states, with energies Eo, E1,... . In this model, atomic excitations are represented by transitions of an electron, bound to the atom, from its ground state energy to a higher level. Excitation to increasingly higher energies is facilitated by energy levels that lie closer together. Eventually, excitation beyond the ionization energy of the atom produces an electron which is no longer associated with the atom. Such an electron enjoys a continuum of available energy states. The essential features of this scheme are represented by an energy-level diagram as shown schematically in Fig. 1. Horizontal lines in this figure represent “allowed” values (measured along the vertical axis) of the total energy (Ekin+Epot) of the most weakly bound electron in the atom. Notice that these discrete values are negative, indicating that these states are “bound” states of the electron; i.e. work has to be done in order to remove the electron from any of these states or “levels”. In particular, the lowest lying level E(0)ground, called the “ground state”, has the largest negative energy. When not excited, the electron and thus the atom stays in the ground state. Removal of an electron from an atom is called “ionization”. Thus, in order to ionize the atom in its ground state, an amount of work equal to -E(0)ground (or larger) has to be supplied to the atom.2“Excitation” of the atom occurs when the electron in its ground state absorbs energy, after which it is promoted to one of the higher bound states E(i)excited. Electrons in atoms can be excited in a number of ways, such as bombarding atoms by free electrons or illuminating atoms by light. Figure 1: A schematic diagram showing the energy levels of an atom. The heavy solid lines represents the vacuum level and separates the quantized states from the continuum. If an atom is supplied with energy by excitation from a free electron, then a bound electron can take up energy from the free electron only in quantized amounts ∆E equal to the difference in energy between the excited level and the ground state. )0()()()(groundiexcitedafterkinbeforekiniEEEEE −=−=∆ )(beforekinE - kinetic energy of the bombarding free electron before collision, )(afterkinE - kinetic energy of the bombarding free electron after collision, )(iexcitedE - i-th excited state of the atom, and )0(groundE - ground state of the atom. If an atom is bombarded with electrons whose kinetic energy are less than the first excitation energy of the atom, no exchange of energy between the bombarding electrons and the electrons bound to the atom can take place. (This of course neglects any small amount of energy that may be transferred in elastic collisions when the whole atom recoils without being electronically excited.) Thus, the electron in the atom remains in the ground state )0(groundE . If )(beforekinE is equal to or greater than )(iexcitedE -)0(groundE , the electron in the atom can be promoted into the first excited state. If a free electron is accelerated through mercury vapor having an appropriate atom number density, the probability of exciting the ∆E1 transition is much larger then exciting any other ∆Ei transition. Thus in a sequence of n collisions with n different mercury3atoms, the bombarding electron can convert n∆E1 energy into atomic excitations. Bohr’s quantum ideas were well supported by many studies of electromagnetic radiation from atoms where photons with definite energies were either emitted or absorbed. The historical significance of the Franck-Hertz experiment is that it provided convincing proof that energies of atomic systems are quantized not only in photon emission and absorption but also under particle bombardment. The energy levels of Hg In this experiment, you will probe the energy levels of a Hg atom. A neutral mercury atom has 80 electrons. These 80 electrons are distributed in a configuration specified by 1s2,2s2,2p6,3s2,3p6,3d10,4s2,4p6,4d10,4f14,5s2,5p6,5d10,6s2. It is convenient to divide these 80 electrons into two broad categories often referred to as inner shell and outer shell electrons. We know that 78 of these electrons reside in inner shells (1s,2s,2p, etc.) and 2 of these electrons reside in the outermost 6s shell. At low energy bombardment, only one of the two outermost electrons in the 6s shell is promoted to an excited state referred to as a triplet 6 3P1 state as shown in Fig. 2. The most probable excitation to this triplet state requires a 4.86 eV energy transfer to the bound electron of the mercury atom. The probability of excitation to higher levels of the 6s electrons or the probability of excitations of any inner shell electron is very low and need not concern you in this experiment.4Figure 2: A term diagram showing the lowest lying energy levels for a mercury atom. In general, the excited states are unstable, and the atom exists in that state only for a short time, typically 1 to 10 nanoseconds. When it returns to the ground state, an amount of energy =E(i)excited-E(0)ground=∆Ei is released in the form of electromagnetic radiation. The wavelength of the radiation