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.
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.
Something is rotten in the state of Denmark. Shakespeare , Hamlet, Act 1 Scene 4 The rise and fall of the old quantum theory The principles of the old quantum theory were first articulated by Niels Bohr in 1913 in a three-part paper titled “On the Constitution of Atoms and Molecules.” Bohr had adopted Ernest Rutherford's model of the atom, according to which the mass of the atom is concentrated in a small central nucleus, while the electrons orbit the nucleus in planetary trajectories. The key challenge facing Rutherford's model was that it was unstable: according to classical electrodynamics, the electron, which is a moving charged body, should radiate energy and so eventually collapse into the nucleus. Bohr's solution was to incorporate Max Planck's theory of radiation, according to which “the energy radiation from an atomic system does not take place in the continuous way assumed in ordinary electrodynamics, but that it, on the contrary, takes place in distinctly separated emissions” (Bohr 1913, p. 4; BCW 2, p. 164). In this early paper, and most subsequent accounts, Bohr summarized his quantum theory by means of two assumptions or postulates. According to the first postulate, electrons cannot travel in any path they like around the nucleus, rather atomic systems can only exist in a series of discrete “stationary states,” in which the electron is in a particular allowed stable periodic orbit and is not emitting radiation.
In 1897, Thomson demonstrated that cathode rays (observed to be emitted from the cathodes of vacuum tubes) were in fact charged particles which he called electrons. Thomson proposed that the atom consisted of a positively charged sphere in which were embedded negatively charged electrons. Rutherford subsequently found in 1911 that the electrons orbited at some distance from a central positively charged nucleus. Rutherford proposed that electrostatic attraction between the nucleus and the electron was balanced by the centrifugal force arising from the orbital motion. However, if this were the case, then the electrons (being accelerated inwards towards the center of rotation) would continuously radiate all their energy as electromagnetic waves and very quickly fall into the nucleus. In 1913, Bohr postulated two important additions to Rutherford’s theory of atomic structure: 1. Electrons can orbit the nucleus in what are called stationary states in which no emission of radiation occurs and in which the angular momentum L is constrained to have values: 2. Electrons can make transitions from one state to another accompanied by the emission or absorption of a single photon of energy E = hf thus leading to absorption and emission spectra.
This chapter illustrates Niels Bohr's ideas in some detail. In the formulation of his model, Bohr assumed that the electron in the hydrogen atom moves under the influence of the Coulomb attraction between it and the positively charged nucleus, as assumed in classical mechanics. The Bohr model was very successful in explaining the discrete atomic spectra of one-electron atoms. The Bohr model is, of course, a theoretical model of an atom. Using Bohr's quantization postulate, find the linear velocity of the electron's sphere. To find the radius of the orbit, Bohr postulated that the angular momentum of the electron is quantized, i.e., it can only take values that are integer multiples of ħ. The chapter begins with considering the classical equation of motion for the electron in a circular orbit, which is based on Newton's laws of motion and Coulomb's law of electric force.
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
In 1913, Niels Bohr developed an accurate model for the hydrogen atom. The mathematics involved and the simplicity of this model is easily understood. The intention of the paper is not to replace Bohr's model, but to find a similar model for all atoms. The model discussed, which was developed on the same basis as Bohr's model for the hydrogen atom, calculates the radii and the energies of the orbits. The wavelength of an emitted photon when an electron makes a ‘jump’ from a higher state to a lower state can also be calculated from the model. Finally, the paper demonstrates that the model obeys the de Broglie's hypothesis that the moving electron exhibits both wave and particle properties.
Many teachers like to introduce the Bohr atom toward the end of an introductory physics course. This is an excellent idea, given the historic importance of Bohr’s 1913 work, which provided the bridge from Planck’s quantized interaction of matter and radiation (1900) to the full theory of quantum mechanics (1925-28). Unfortunately, the version of the Bohr atom that appears in many textbooks and is no doubt often presented to students is more wrong than right and may leave both teachers and students wondering why, more than a hundred years later, it is still being taught. This “pedagogic” version postulates that an electron in a stationary state moves in a circular orbit with an angular momentum that is an integral multiple of h/2π (L = nh/2π = nħ)—ħ for the lowest-energy state, 2ħ for the next state, and so on. This picture of the hydrogen atom is wrong in two senses. First it doesn’t conform to our present understanding of the hydrogen atom. This, in itself, is not a reason to scrap it, for the historical development of quantum physics is certainly of interest. But second, it doesn’t conform to the essence of what Bohr actually did. That is a reason not to teach about circular orbits and L = nħ.