RESONANCE POTENTIALS. We are brought to the consideration of resonance potentials, which are also called crit ical potentials or excitation potentials, by the consideration of the passage of an electron through a gas. We must first premise that the energy, and consequently the velocity, of an electron is usually expressed in volts, a velocity of so many volts meaning the ve locity which an electron would acquire in moving freely through a potential difference of that number of volts. It has been estab lished by the experiments of J. Franck and G. Hertz that electrons of small energy, i.e., with velocities of a few volts only, behave like minute gas atoms when they strike a gaseous atom. The im pact follows the laws of the impact between two perfectly elas tic spheres, the electron bouncing off with practically no loss of velocity, since the mass of the gas atom is relatively so great. When we are considering the passage of electrons through inert gases, metallic vapours of small electron affinity, and certain other gases, it is found, however, that, as the velocity of the electrons is raised, a certain critical value is reached; for all velocities greater than this critical velocity the electron loses a definite amount of energy in the collision, or makes what is known as an inelastic impact. The kinetic energy so lost goes temporarily to increase the internal energy of the atom, and ultimately appears in some other form. If the velocity of the electron be further increased the loss of energy at impact remains the same until a step is reached when another sudden loss of energy takes place on impact, this time of greater magnitude. In general, as the potential which accelerates the electron is increased a series of values will be found, at each of which a different type of inelastic collision with the gaseous atom first takes place. These particular values are the resonance poten tials characteristic of the gas in question : they vary in magnitude from gas to gas. Finally, a potential can be found which gives the electron sufficient energy for it to be able to ionise the gas atom which it strikes, that is, displace an electron from it. This poten tial is the ionisation potential of the gas.
Theoretical Importance of Resonance Potentials.—The resonance potentials have assumed great importance in modern physics from the direct confirmation which they give of the most fundamental assumption of Bohr's theory of atomic structure. (See ATOM, QUANTUM THEORY.) On this theory an atom can exist in a series of stable states—or stationary states, as they are called —to each of which pertains a given energy, but cannot exist in any state of energy intermediate between these. We can get a picture of these states by assuming that the electrons of the atomic structures have certain preferential orbits, to each one of which corresponds a certain energy of the atom (see ATOM), but this picture is not indispensable for our present purpose. To transform
the atom from its normal state, of energy E, to a stationary state of greater energy E', clearly demands a certain input of energy : when the atom returns from this excited state to its normal state —either in one step or more steps—the energy is given out again, in general in the form of radiation (in general, because it is possi ble for the energy to appear as kinetic energy of another particle), the frequency of the radiation being given by where h is Planck's constant, v the frequency. We should there fore expect that if an electron strikes an atom, and its energy is less than that required to raise the atom to the first stationary state above the normal, it will be unable to communicate any thing to the internal energy of the atom, and will spring off elas tically. If, however, the energy E. of the electron in question equals or exceeds where is the energy of the first sta tionary state, it can raise the atom to that stationary state, and will proceed of ter the collision with diminished energy We neglect the kinetic energy communicated to the atom as a whole, since, on account of the great mass of the atom, this is negligible. Similarly, if the energy of the electron exceeds E, when is the energy of the second stationary state, the electron can raise the atom to that state, experiencing itself a correspond ingly greater loss of energy. In the first case the atom, on re turning to its normal state, should emit the first spectral line of a series, in the second case the second line, of higher frequency, and higher critical potentials should be able to excite lines of still higher frequency. The resonance potentials therefore provide a double experimental check on Bohr's hypothesis. In the first place we can, by electrical methods, measure the velocity of the elec tron before and after impact with the gas atom, observe at what potentials the abrupt losses of velocity take place, and compare these potentials with those to be anticipated from the known values of hv for the appropriate lines of the spectrum of the atom. In the second place we can observe the radiations from the gas which attend the passage of electrons of different velocities, and find out at what potentials the different lines first appear—i.e., we can carry out the so-called step-by-step excitation of spectra, and measure the excitation potentials. Both methods lead to brilliant quantitative confirmation of Bohr's hypothesis of sta tionary states, and of the quantum theory of spectral series. The electrons lose energy in steps, at the stages to be anticipated from the theory, and the spectral lines appear in turn at the potentials calculated.