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The Franck{Hertz Experiment

Michael S. Turner, James W. Waters

Published Jan 1, 2002• 0 citations

Abstract

In 1912 Niels Bohr developed his model of the atom, in which electrons are allowed only certain discrete orbits. Transitions between these orbits may take place only when the atom absorbs or emits quantized packets of energy E = hc. This explains the spectral lines given o ® by an excited element, such as described by Rydberg's formula for the series of spectral lines for hydrogen. Less than a year after Bohr published his theory, J. Franck1 and G. Hertz2 proved it experimentally, earning themselves the 1925 Nobel Prize in Physics. They boiled electrons o ® a hot ¯lament K, used a potential Ub to accelerate them through a vapor of an element toward a grid A (v. Fig. 1), and looked for them on a plate M, with a small retarding potential V0 = 1.5 V, to stop electrons whose kinetic energy was below a certain value. Figure 1: Circuit diagram for the Franck-Hertz experiment If the kinetic energy of the electrons is too small to excite the atoms in the vapor, the electrons collide elastically and lose almost no energy, as required by the conservation of energy and momentum, and a large current is detected at plate M. If, on the other hand, the electrons gain just enough kinetic energy 1James Franck, American (German-born) physicist, 1882-1964 2Gustav Hertz, German physicist, 1887-1975, nephew of Heinrich Hertz, who discovered radio waves

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In 1912 Niels Bohr developed his model of the atom, in which electrons are allowed only certain discrete orbits. Transitions between these orbits may take place only when the atom absorbs or emits quantized packets of energy E = hc. This explains the spectral lines given o ® by an excited element, such as described by Rydberg's formula for the series of spectral lines for hydrogen. Less than a year after Bohr published his theory, J. Franck1 and G. Hertz2 proved it experimentally, earning themselves the 1925 Nobel Prize in Physics. They boiled electrons o ® a hot ¯lament K, used a potential Ub to accelerate them through a vapor of an element toward a grid A (v. Fig. 1), and looked for them on a plate M, with a small retarding potential V0 = 1.5 V, to stop electrons whose kinetic energy was below a certain value. Figure 1: Circuit diagram for the Franck-Hertz experiment If the kinetic energy of the electrons is too small to excite the atoms in the vapor, the electrons collide elastically and lose almost no energy, as required by the conservation of energy and momentum, and a large current is detected at plate M. If, on the other hand, the electrons gain just enough kinetic energy 1James Franck, American (German-born) physicist, 1882-1964 2Gustav Hertz, German physicist, 1887-1975, nephew of Heinrich Hertz, who discovered radio waves

Niels Bohr made numerous contributions to physics. But his most important was to break the rules. Bohr propounded several postulates. First, that electrons revolved in their orbits around the nucleus of an atom without emitting energy. Second, that spectral lines came from electrons emitting energy by jumping from one orbit to a lower one. Third, that only certain orbital radii were allowed. All three of these unsubstantiated claims violated classical physics, according to which accelerating charges emit energy. Thus, electrons should lose their energy and spiral into the nucleus. But this theory could not account for spectra; Bohr's postulates could. Bohr was the leader of a brilliant group of physicists who developed most of the fundamentals of quantum mechanics and showed that its laws proved the validity of his inspired guesses. A non-member of the group was Einstein, who disagreed with his friend Bohr over the actual meaning of quantum mechanics.

Most textbooks say that quantum mechanics came into being when Max Planck, in a desperate attempt to construct a theory that explained experimental data, explored the radical idea of energy being radiated or absorbed by all bodies in discrete packets (or quanta). The energy content of a quantum of radiation is proportional to the frequency of the radiation emitted or absorbed, as in , and the proportionality constant bears the name of Planck. Planck himself was rather uncomfortable with the idea of energy packets, and spent a considerable amount of time in later years trying to “restore” the classical picture of continuous energy exchange between bodies and surroundings. However, in 1905 Einstein was able to use the idea of the quantum to explain the mechanism of the photoelectric effect, which cannot be explained in any other way! This established the reality of the quantum and so, it may be said that Einstein, rather than Planck, is the father of quantum mechanics. Within a few years, Neils Bohr constructed his model of the hydrogen atom in which the electron can only occupy certain special orbits around the nucleus, and any jump between these orbits is accompanied by energy being absorbed or emitted in the form of quanta. The nearly exact agreement of Bohr’s predictions based on the model and observed hydrogen atomic spectra was among the first impressive accomplishments of quantum mechanics.

1913 est l’annus mirabilis de Niels Bohr. Il écrit sa « trilogie », fondatrice de son modèle d’atome, toujours en vigueur de nos jours. C’est le premier de ces trois articles qui est commenté ici. 1/ Il y applique la théorie quantique, en inférant que le rayonnement d’un électron tournant autour du noyau est émis par quanta d’énergie égaux à un multiple de hν (où h est la constante de Planck et ν est la fréquence du rayonnement). Ses résultats étaient conformes aux ‘séries de Balmer‘ du spectre d’émission de l’hydrogène. L’année suivante (1914), l’expérience de Franck et Hertz (collisions d’électrons et d’atomes de mercure) prouvera de manière irréfutable que les électrons perdent de l’énergie par quanta, et que les atomes de mercure émettent du rayonnement ultraviolet dont la fréquence est celle calculée par la théorie de Bohr. 2/ Il y donne l’expression des rayons d’orbites électroniques et de leur niveau d’énergie, indexés par un nombre n (quantification des orbites). 3/ Il y esquisse une première approche et une utilisation féconde du principe de correspondance : le comportement d’un système décrit par les lois de la physique quantique obéit aux lois de la physique classique si le système est suffisamment grand.

Through his experiments, the physicist Niels Bohr improved upon Rutherford's model of the atom and developed his model of the atomic structure in 1913 that succeeded in explaining the spectral features of the hydrogen atom. A simple means for extending the conventional non-relativistic Bohr model of the atom to include the wave nature of electrons is presented. As the derivation requires basic knowledge of classical and wave mechanics, it can be taught in standard courses in modern physics and introductory quantum mechanics.

One hundred years ago the physics that would be necessary to understand how quantum computers work, much less how to build them, did not exist. In the early 1920s electrons were viewed as tiny negatively charged particles—microscopically small spheres—with energies and locations within an atom that were well defined. In Niels Bohr’s Nobel-prize-winning atomic model, electrons moved in orbits around the nucleus with their energy and position both known with, to many scientists, reassuring certainty. Quantum computers rely for their operation on the uncertainty, the “weirdness”, that happens on the atomic scale and below.

The existence of line spectra can be explained bymeans of the first “quantum”model of the atom, developed by Bohr in 1913. Although the Bohr model of the hydrogen atom was eventually replaced, it yields the correct values for the observed spectral lines, and gives a substantial insight into the structure of atoms in general. The following derivation has the objective of obtaining the energy levels of the Bohr atom. If we can obtain the energy levels, we can reproduce the hydrogen atom spectra. The derivation proceeds with three major elements: first, use force balance to relate the velocity to the radius of the electron orbit, then use a quantum assumption to get the radius, then solve for the energies.