Three Scientific Revolutions: How They Transformed Our Conceptions of Reality (24 page)

Concluding that it would be “hopeless” to try resolving these problems in terms of classical mechanics, Bohr decided to incorporate Planck and Einstein's quantification of radiation in his calculations. Like others at the time, initially he conceived the electrons as “atomic vibrators” that radiated according to Planck's quantum of action as Bohr wrote in one of his famous articles published in 1913:

According to Planck's theory of radiation . . . the smallest quantity of energy which can be radiated out from an atomic vibrator is equal to
vk
, where
v
is the number of vibrations per second and
k
(we now called it
h
) is Planck's constant.
Thus did the quantum theory enter the interior of the atom for the first time.
⁸⁴

But the difficulty was acquiring the empirical data that would contribute to solving the problem. During the short time Bohr was at the Cavendish Laboratory he probably met John Nicholson, a gifted young researcher who in 1911 “associated spectral lines with various modes of vibration of electrons around their equilibrium orbits in the field of a central charge.”
⁸⁵
In another article he proposed that the angular momentum of a revolving electron could be calculated from the mass, velocity, and the radius of its orbit. As Pais states: “If, therefore, the constant
h
of Planck has . . . an atomic significance, it may mean that the angular momentum of an atom can only rise or fall by discrete amounts when electrons leave or return” (p. 199).

But it was a suggestion of a student friend that led Bohr to consider the possible effect of electron orbits (rather than atomic oscillations) on the spectral emissions that produce the frequencies, especially in connection with Johann Balmer's radiational formula introduced in 1885. The latter depicts the related mathematical frequencies of light emitted by hydrogen into a small number of series that provide the crucial insight. As Bohr recalled many years later: “As soon as I saw Balmer's formula the whole thing was immediately clear to me. . . .”
⁸⁶

What Bohr immediately realized was that Planck's constant of action
h
at 6.62 × 10
^-27
erg-seconds was the key to solving the problem of the orbits of electrons if he included it in his formula. Because
h
has a fixed value, by inserting it meant that the electron's orbits could only take on specified values that were multiples of Planck's constant. In addition, this indicated that any change from one orbit to another would require an exchange of energy: the absorption of energy if the electron jumped to a higher orbit or a discharge of energy if the electron dropped to a lower orbit. Furthermore, he inferred that since the exchange of energy came in a predetermined amount, it must be a form of electromagnetic radiation and also that E =
hv
meant the radiation involved definite frequencies since
v
stands for frequencies.

Thus Bohr's solar model of the atom consisted of electrons surrounding the nucleus in a series of orbits called “stationary states” whose
locations
were dictated by Planck's constant but whose
orbital trajectories
were determined by their angular momentum and energy or frequency. The emissions originated from a spaceless “jump” of the atomic electrons from one orbital or energy level to another. This also showed that not all transmutations originate in the nucleus as previously believed.

But there remained the original problem of why, according to classical physics, the electron at the lowest orbital state was not drawn into the nucleus by the electrostatic force eventually overcoming the energy of its angular momentum. This was solved by Bohr simply declaring that the “ground state is stable,” which Pais describes as “one of the most audacious postulates ever seen in physics.”
⁸⁷

Bohr's explanation was also “audacious” because it incorporated classical and quantum mechanics in an unorthodox way: he described the
energy
or
frequencies
of the particles' angular momentum in terms of
classical
mechanics
, while the
optical
frequencies
of the ejected photons were described wholly in terms of
quantum
mechanics
. This use of two conflicting mechanistic explanations, although related to different kinds of frequencies, is the first evidence of the two principles that would guide Bohr's interpretation of quantum mechanics: the “correspondence principle” and the “principle of complementarity.”

Where the magnitudes of the frequencies of the
electrons
in the successive orbits resemble classical magnitudes the calculations tend to “correspond,” but where the magnitude of the
optical
frequencies of the ejected photons is much greater they tend to be “complimentary.” While unorthodox, the solution is similar in physics where relatively slow velocities are computed in terms of Newtonian mechanics and the greater optical velocities are computed by Einstein's relativity theory.

Despite his model being largely theoretical, the derivations Bohr was able to infer from them were amazing, such as Balmer's formula, Rydberg's constant, deducing the radius of the bound state of the stable hydrogen atom (called the “Bohr's radius”), and especially demonstrating that a series of stellar spectral lines that had been attributed to hydrogen were in fact the spectral lines of ionized helium.

In addition to these computational achievements, he was able to devise a number of new theoretical explanations of spectral emissions using such theories as blackbody radiation, the photoelectric effect, nuclear radioactivity, electron radiation, and spectroscopy. Also, by dividing the electron orbits into outer and inner shells he could attribute visible spectra to the outer electron shells while X-rays he explained were due to an electron being ejected from an inner shell. Beta rays, later identified as electrons, he correctly attributed to radioactive decay in the nucleus.

Although the above is just a cursory summary it does convey something of the magnitude of his accomplishments. Similar to Einstein's five publications in 1905, at the early age of twenty-five, that revolutionized Newtonian mechanics, Bohr's three publications in 1913 when he was twenty-eight years old on the orbital structure and function of electrons revolutionized atomic physics. Pais summarizes Bohr's accomplishments:

The very existence of line (and band) spectra suggests, he noted, that electrons move in discrete stationary orbits inside atoms and molecules. Spectra (including X-ray spectra) arise because of quantum jumps between these states. . . . The quantitative confirmation of these ideas by his treatment of hydrogen and ionized helium mark a turning point in the physics of the twentieth century and the high point in Bohr's creative career. The insistence on the role of the outermost ring of electrons as the seat of most chemical properties of the elements, in particular their valencies, constitutes the first step toward quantum chemistry. The sharp distinction between atomic/molecular and nuclear physics begins with his realization that β-rays emanate from the nucleus.
⁸⁸

The response to these innovations, called the “Copenhagen interpretation,” were diverse with Rutherford, Arnold Sommerfeld, and Moseley favorable, while Otto Stern and Max von Laue declared, after reading Bohr's 1913 article that, “if by chance it should prove correct, they would quit physics” (though they later changed their minds). It was Einstein who paid the most eloquent tribute becoming a close friend and admirer of Bohr despite his strong aversion later to quantum mechanics.

That this insecure and contradictory foundation was sufficient to enable a man of Bohr's unique instinct and tact to discover the major laws of the spectral lines and the electron shells of the atoms together with their significance for chemistry appeared to me like a miracle—and appears to me as a miracle even today. This is the highest form of musicality in the sphere of thought.
⁸⁹

But Bohr, aware of its ad hoc nature was somewhat uncertain of his theory of the hydrogen spectra, yet because of the general agreement of his solar model of the atom with the experimental evidence and consistency with other quantitative derivations, he accepted it as a provisional theory despite knowing that, due to the uncertain nature of the measurements, it lacked a definitive internal structure and firm independent reality. Still, as Pais indicates, his achievements were exceptional.

As the year 1913 began, almost unanimous consensus had been reached, after much struggle, that atoms are real. Even before that year it had become evident that atoms have substructure, but no one yet knew by what rules their parts moved. During that year, Bohr, fully conscious that these motions could not possibly be described in terms of classical physics, but that it nevertheless was essential to establish a link between classical and quantum physics, gave the first firm and lasing direction toward an understanding of atomic structure and atomic dynamics. In that sense he may be considered the father of the atom.
⁹⁰

Although at the time Bohr's solar model of the atom was mainly conjectural, its authenticity was reinforced by the supporting discoveries it engendered, to which we now turn. Among the things he could not explain was the reason that electrons in the hydrogen atom were restricted to their particular orbits and why their angular momentum was an integral multiple of Planck's constant
h
, or depict the atomic spectra of atoms with an electronic structure more complex than hydrogen. This awaited the discoveries of the “new quantum theory,” in contrast to Bohr's “older quantum theory,” begun in 1923 as a result of the successive contributions mainly of A. H. Compton, Louis de Broglie, Werner Heisenberg, Paul Dirac, and Erwin Schrödinger, along with Wolfgang Pauli, Pascual Jordan, and Max Born.

One of the first to begin the transition was Prince Louis de Broglie who, assisting his older brother Duke Maurice in his experiments on the dual properties of light, presented in 1923 his doctoral dissertation to the French Academy of Sciences on “The Connection between Waves and Particles.” Recall that to explain blackbody radiation Planck had introduced in 1900 the concept of the “quantum of energy” to designate the discontinuous or discrete
exchange of energy
caused by the light waves striking the oscillating electrons within the metal to produce the ejected electrons, but he had restricted it solely to the
interaction
occurring
within the metal
. In contrast, in 1905 Einstein explained the photoelectric effect as not due to
light waves
striking the metallic surface but to a stream of
light particles
colliding with the electrons within the metal, which light particles were later named “photons.”

Having no mass, in order to eject the electrons from within the metal the light particles had to possess a certain quantity of energy that Einstein defined as
hf
(Planck's constant
h
times the light frequency
f)
per particle. So, though light produced diffraction patterns characteristic of waves when injected through a tiny aperture, it also displayed the properties of particles when reflected on metals causing an interaction with the inner vibrating electrons. This duality of contrary properties introduced one of the two main paradoxes of quantum mechanics, the other being the uncertainty of the measured properties.

The duality was further evidenced when in 1922 the American physicist Arthur Compton discovered that when paraffin was irradiated with X-rays a portion of the emerging waves had longer wavelengths than the entering ones. Compton believed the effect was not explainable by the usual wave theory of electromagnetic radiation but could be explained if light consisted of quanta of energy some of which was transmitted to the electrons in the paraffin due to the collisions. So even if the light quanta do not have mass, they do have momentum owing to the energy.

His experiment showed that “a photon of electromagnetic radiation of wavelength λ carries momentum whose value is
p
=
h
/λ, where
h
is Planck's constant, λ the wave length, and
p
the momentum. Compton explained that in the collision with an electron the photon loses momentum, and therefore its wavelength increases by the scattering.”
⁹¹
Thus the explanation of blackbody radiation, the photoelectric effect, and Compton's experiment reinforced the validity of the dualism of light despite the paradoxical contradiction of properties.

Intrigued by light having particle properties, de Broglie decided to investigate as his dissertation subject whether the converse was true, that particles could have wave properties. Ne'eman and Kirsh summarize his revolutionary theory as follows.

Every moving particle has an associated wave of definite wavelength and frequency determined by the mass and velocity of the particle. The laws of motion of small particles cannot be understood unless the wave nature of the particles is taken into account, just as the photoelectric effect and black body radiation cannot be understood without resort to the particle properties of light.

The mathematics of this model was simple. De Broglie assumed that the equations
E
=
hf
and
p
=
h
/λ were valid for material particles as for photons. Thus, the wavelength, λ, of the particle is given by λ =
h
/
p
where
p
is its momentum. The faster the particle moves, the shorter is its wavelength. (pp. 39–40)

De Broglie's dualistic theory contributed to Bohr's orbital model of the atom by explaining that if electrons possessed wave properties, the circumference of the orbital circle would have to be an integral number of wavelengths, otherwise they would interfere and destroy. He also calculated the angular momentum of the circular orbits of the electrons that could be observed in a cloud chamber. Yet other questions pertaining to Bohr's model were still unexplained: why the electrons in the hydrogen atom were restricted to their particular orbits? what accounts for their orbital jumps? and what were the atomic spectra of atoms that had an electronic composition more complex than hydrogen?