v1.0.2 / chapter 5 of 20 / 01 aug 09 / greg goebel / public domain
* The Rutherford nuclear atom had been a big step forward, but much remained to be learned about the structure of the atom. Further experiments by Rutherford's students and others gave clues that led to the discovery of a new nuclear particle, the neutron. That led in turn to considerations of the "strong force" that held the nucleus together, and the possibility that there was matter of reversed electrical polarity, or "anti-matter".
* While the theoretical physicists were arguing out the details of quantum mechanics, the experimental physicists were continuing to probe into the atom. The Rutherford-Bohr atom consisted of negatively-charged electrons orbiting around a positively-charged nucleus, which Rutherford and his crew would identify as at least partly composed of protons.
Since the late 18th century, chemists had been identifying various elements and classifying them into the periodic table by their atomic weights, which as it turned out could be closely represented by integer multiples of the weight of a proton. That suggested that as elements grew heavier, their nuclei incorporated increasing numbers of protons. One of the oddities was that the atomic weights tended to increase irregularly, usually by a value of two proton masses for the lighter elements, but by increasingly large steps for heavier elements.
In 1911, the British physicist Charles Glover Barkla (1877:1944) had conducted experiments on the production of X rays by bombarding anodes made of different metals with an electron beam. He discovered that different types of metals would produce X rays with different energies, a discovery that won him the Nobel prize in 1917. Rutherford's student Henry Moseley (1885:1915) went further with the idea, observing that the energy of the X rays increased as the elements grew heavier, but not at the same rate as the atomic mass. He suggested that the energy was actually proportional to the net positive charge of the nucleus, in terms of integer multiples of the charge of the proton. The greater the positive charge on the nucleus, the greater the deceleration of the electron, resulting in the emission of a more powerful X-ray photon.
The size of this positive nuclear charge became known as the "atomic number"; it was equivalent to the number of electrons in orbit around a neutral atom. Moseley suggested that the elements were ordered in the periodic table by their atomic number, which increased by a value of 1 for every successive element in the table. Now the periodic table started to make more sense.
Moseley's brilliant insight might have won him the Nobel prize, but with the outbreak of the First World War he went into the ranks of the British Army as a military engineer, to be killed in action during the disastrous landing at Gallipoli in Turkey. He remains a minor figure in the history of physics, but those who knew him and his work believed he had top potential. Robert Millikan wrote that the loss of Moseley all by itself made the conflict "one of the most hideous and irreparable crimes in history."
* To further complicate the picture of the atom, in 1913 Rutherford's student Frederick Soddy had shown that there were different forms, or "isotopes", of the same sort of atoms. Soddy observed that there were some forms of uranium that were much more radioactive than others, even though all the forms were essentially identical in their chemical properties. He won the Nobel prize in 1921 for this discovery. As it turned out, isotopes shared a common atomic number but had different atomic weights. Uranium, for example, had an atomic number of 92, but had two primary isotopes, one with an atomic weight of 238 and another with an atomic weight of 235. These can be shorthanded as "U<238/92>" -- with the "238" read as a superscript and the "92" read as a subscript -- and "U<235/92>".
A relatively straightforward means of separating isotopes, known as a "mass spectrograph", was developed in 1919 by the British chemist Francis William Aston (1877:1945), one of J.J. Thomson's students. In the mass spectrograph, atoms are ionized, accelerated by an electric field, and thrown around a curve in a magnetic field to strike a target containing a set of detectors in a row. Their paths will vary slightly according to their masses and so different isotopes will fall into different detectors. Aston won the Nobel prize for chemistry in 1922; over the next two decades, he would sort out over two-thirds of the 282 naturally-occurring isotopes.
Some elements, such as sodium, aluminum, cobalt, and gold, have no isotopes normally observed in nature; others may have up to a half-dozen. The presence of isotopes had complicated the discovery that the nucleus of the atom was made up of elementary particles such as protons. In 1815, the British chemist William Prout (1785:1850) had suggested that all atoms were composites of hydrogen atoms, but his idea didn't pan out because estimates of the relative mass of elements in bulk showed they didn't have nice neat integer multiples of the mass of the hydrogen atom. The discovery of isotopes explained this: as Aston pointed out, elements obtained in purified bulk form included several isotopes, and the weights obtained were an average.
* By this time, the physicists were beginning to trace out the steps of various radioactive decay processes, observing the transformations of elements into their "decay products" as they released alpha particles (helium nuclei) and beta particles (electrons). Radioactive elements also emitted gamma radiation, but this only released energy and did not in itself lead to a transmutation of an element. Researchers were able to identify chains or "radioactive series" in these decay processes. The series could be complicated, with one radioactive element decaying to another radioactive element, and so on, until the decay chain finally came to rest in a stable element.
The researchers also began to measure the rates of decay for each step in the series. In keeping with the general spirit of quantum phenomena, there is no way to determine exactly how long it takes one atom of a radioactive element to decay into another, but for large numbers of such atoms the decay rate is very predictable. The radioactive decay rate is given traditionally in "half-lives", the amount of time it takes for half a given amount of radioactive material to decay. If such a material has a half-life of, say, two years, in two years there will be only half of it left; in four years, only a quarter; in eight years, only an eighth; and so on. Such an "exponential" decline implies that there will always be some "die-hards" among the atoms in the material that will stubbornly refuse to decay, though at some point they will become all but undetectable.
* By the late 1920s, there was a general belief that the nucleus of the atom consisted of one or more protons along with a lesser number of electrons embedded in that nucleus, resulting in a nucleus with a net positive charge. In radioactive decay, emission of an alpha particle would remove four protons and two embedded electrons from the nucleus, reducing the atom's atomic weight by four and atomic number by two; or emission of a beta particle would remove one embedded electron, leaving the atomic weight essentially the same but increasing the atomic number by one. This concept had the virtue of explaining how the nucleus held together. After all, if the nucleus was nothing but positively-charged protons, their mutual electrostatic repulsion would tear the nucleus apart, and the Universe would consist solely of hydrogen atoms. The embedded electrons, it seemed, "glued" the nucleus together.
This was sort of right, but not exactly on target. There were two problems with this model. The first was that, for the larger atoms, it was difficult to get the sums of the weights of the protons and electrons to come out to the observed value of the weight of the nucleus. The second, more important problem was that the spins of the particles didn't add up. For example, a nitrogen-14 nucleus has a spin of +/-1. Protons, like electrons, are fermions and have a half-integer spin of +/-(1/2). If the nitrogen-14 nucleus honestly consisted of 14 protons and 7 electrons, that meant 21 particles with half-integer spin, and there was absolutely no way to get them to add up to an integer spin.
The way out was to get rid of the 7 electrons and build the nucleus out of 7 protons and 7 particles that looked just like protons, but were electrically neutral. Instead of having discrete protons bound to discrete electrons in the nucleus, somehow the two might be merged together, forming a single particle in which the opposed electrical charges of the two balanced out. Rutherford had suggested this idea in 1920, and in 1921 the American chemist William Draper Harkins (1871:1951) named this particle the "neutron", meaning more or less "neutral proton". At the time, Harkins' neutron was a purely hypothetical beast, and most physicists didn't believe in it.
In 1930, a German physicist named Walter W.G.F. Bothe (1891:1957) and his colleague Hans Becker bombarded beryllium metal with alpha particles and managed to produce some sort of energetic radiation that was electrically neutral; for lack of a better idea, they suggested it was gamma radiation. In 1932, two French physicists, Frederick Joliot-Curie (1900:1958) and his wife Irene Joliot-Curie (1897:1956) -- Irene was the daughter of Pierre and Marie Curie -- published results of their experiments on this radiation. They found it ejected protons from a block of paraffin -- candle wax -- which was rich in hydrogen atoms as a source of protons. Gamma rays didn't seem adequate for the task but the Joliot-Curies couldn't think of an alternative.
The British physicist James Chadwick (1891:1974) pursued the same line of investigation, but he was already hunting for the neutron and believed that the Joliot-Curies had, unknown to them, found the beast. Obviously, if this energetic radiation could eject protons, it had to be about as heavy as a proton; gamma rays simply didn't have the kick needed to do the job. Since the particles that made up the radiation were electrically neutral, that meant the particles were neutrons.
Of course, he needed proof, and it had to be good proof lest he fall into the only-too-tempting trap of misinterpreting poor data just because he wanted to believe it. Chadwick duplicated the experiment performed by the Joliot-Curies, first obtaining protons from a block of paraffin, then substituting a wide range of other atoms for the paraffin. He got much the same results and published them immediately. The Joliot-Curies were deeply humiliated when they read Chadwick's report and realized that they had been overlooking the obvious.
Chadwick won the Nobel prize in 1935 for this discovery. It took much longer to find the neutron than the proton because particle detector technologies developed up to then were only suited to tracking down charged particles; neutral particles like photons and neutrons don't leave ionization trails, and they can only be detected by direct interactions, in other words by slamming them into something. The neutron would prove to be very slightly heavier than the proton, by about 0.14%, with a mass of 1.675E-27 kilograms. Incidentally, protons and neutrons are collectively referred to as "nucleons".
* The discovery of the neutron made the concept of isotopes easier to understand: the nucleus of an atom of a particular element always contained the same number of protons, but it might contain different numbers of neutrons. For example, the nucleus of ordinary hydrogen contains only a single proton, but about one in every 7,000 hydrogen atoms has a nucleus with a proton and a neutron. This isotope is known as "deuterium" or "heavy hydrogen". Deuterium is a stable isotope; it does not undergo radioactive decay.
There is also an isotope of hydrogen with two neutrons, called "tritium", that is unstable, decaying with a half-life of 12.26 years into the helium-3 isotope, with two protons and one neutron. Helium-3 is stable but is about a million times less common than normal helium-4, which has a nucleus consisting of two protons and two neutrons. Of course, this is the same as the alpha particle.
All atoms of each particular element have, effectively by definition, the same number of protons, but the isotopes of an element have, again effectively by definition, a different number of neutrons. Uranium, near the other end of the periodic table, has 92 protons, with several isotopes: the most common, U<238/92>, has 146 neutrons, while the second most common, U<235/92>, has 143 neutrons.
* The discovery of the neutron unsurprisingly led to more questions. If the nucleus didn't contain electrons to glue it together, then how did the nucleus keep from flying apart? The neutron very likely had something to do with it, but what? There were also the related questions of why elements became more unstable as their atomic number increased, and why the ratio of neutrons to protons generally increased with atomic number as well.
In 1932 Heisenberg suggested that the nucleus was held together by a "strong force", proposing that the protons and neutrons in a nucleus were impermanent: a neutron could pass an electron to a proton, with the neutron then becoming a proton and the reverse. This process would be going on at a great rate at all times, and the net effect would be a strong attractive force. However, neutrons, protons, and electrons are all spin-1/2 particles, and so this implied that either the spin was magically created out of nothing, or that these electrons were spin-0 particles. Few were enthusiastic about Heisenberg's speculations.
However, other options were available. In the late 1920s, Paul Dirac had been working on the Schroedinger equation, revising it to be compatible with Einstein's theory of relativity. The "Dirac equation", as it was known, was a superset of the Schroedinger equation that reduced to the Schroedinger equation when the velocities of particles in the system being described were low. Dirac then used that work as a springboard for consideration of origins of the electromagnetic field in a quantum context. Quantum mechanics asserted that electromagnetic energy was carried in discrete packets, the photons; this implied, as Enrico Fermi and others pointed out, that the electromagnetic field, which set up a force between two charged particles, actually amounted to exchanges of photons between those two charged particles.
The photon was the "exchange particle" that mediated the electromagnetic
force. These photons were created even though the energy to produce them
wasn't present. This violation of energy conservation was permitted because
the Heisenberg uncertainty relation:
delta_energy + delta_time >= hbar
-- provided a dodge: a particle of a given energy could be spontaneously
produced, but only as long as it didn't live long enough to be detected. Of
course, the higher the energy, the shorter the time of its existence. Such
photons were called "virtual particles".
It is intuitive that two charged particles could generate a repulsive force by bouncing photons off of each other, but Dirac's analysis showed that they could generate an attractive force as well. This being counterintuitive, photons sometimes called "messenger particles" instead of exchange particles, on the rationale that they send a "message" between two charged particles to tell them to fly apart or to come together.
The shy, brilliant Japanese physicist Hideki Yukawa (1907:1981) began to tinker with the notion that the strong force might also involve an exchange of particles. Yukawa initially suspected that the force that held the nucleus together was mediated by rapid exchanges of photons, just as photons mediated the electromagnetic field. The problem with this idea was that a strong force based on photon exchanges would have been detectable outside of the nucleus, and the strong force was not: it clearly only worked at the very close ranges inside the nucleus. Electromagnetism and gravity fall off in an inverse-square fashion -- double the distance and the force is reduced by a factor of four -- but the supposed strong force clearly fell off very rapidly. If gravity behaved in the same way, we could become weightless by walking up the stairs of a building.
The photon is the mediating agent of the electromagnetic field, and physicists believe that the gravitational field is mediated by a particle as well, named the "graviton", though its action is so subtle that it has never been detected. These particles are massless, travel at the speed of light, and nothing interferes with their motion through free space; simple considerations of geometry lead to their inverse-square range law. Yukawa believed that the short range of the strong force could be explained if the exchange particle was massive.
Yukawa's exchange particle was a virtual particle, governed by the Heisenberg
uncertainty relation:
delta_energy + delta_time >= hbar
Since, according to Einstein's theory of relativity, nothing could exceed the
speed of light, the amount of time Yukawa's particle could exist could be
no more than the range of the strong force divided by the speed of light.
Plugging this into the relation gave:
delta_energy + range_strong_force / speed_of_light >= hbar
This gave the minimum energy of Yukawa's particle as:
delta_energy = hbar - range_strong_force / speed_of_light
By Einstein's mass-energy equivalence E = MC^2, the delta_energy meant a
particle about 15% as massive as the proton, or 200 times more massive that
the electron. This particle would be exchanged between nucleons, changing
protons to neutrons or the reverse.
Photons are massless, and so people could swallow their "virtual" creation and absorption by charged particles. The idea of Yukawa's large particles being created and absorbed by nucleons on a continuous basis seemed bit more of a stretch. However, the real problem with Yukawa's theory was that nobody knew of any such particle at the time, leading him to suspect he was on the wrong track, but he went ahead and published his results anyway in 1935. If he was wrong -- well, maybe somebody would be able to tell him where his blunder was.
At first, the reaction of the physics community to his ideas was indifferent at best, critical at worst; on a visit to Japan, Niels Bohr told Yukawa: "You must like to invent particles." Indeed, a Swiss physicist named Baron Ernst C.G. von Stueckelberg (1905:1984) came up with much the same theory in parallel, but Wolfgang Pauli savaged the idea so badly that Stueckelberg didn't bother to publish. Yukawa would be vindicated, but it would be by nothing resembling a straightforward path.
* Yukawa's assertion that the strong force was based on the exchange of unknown particles suggested the simple set of known particles was incomplete. Paul Dirac suggested that there might be a few other unknown particles as well.
Dirac's work on his relativistic version of the Schroedinger equation had an interesting if troublesome result: electrons could have "negative energy" states just as they had positive energy states. Nobody was exactly sure what negative energy was, and to make things particularly troublesome, there was no limit to the negative energy of an electron. To be sure, there isn't really any limit on the positive energy of an electron, but that's like saying that the only limit on how high something can be thrown is the energy available to do it; in practice, the energy will never be unlimited. The lack of limit on the negative energy of the electron was equivalently like saying electrons could fall into a literally bottomless pit, and if that was the case -- then why hadn't they all done so?
Dirac's solution was ingenious, to use one word for it. He asserted that the reason electrons didn't fall down into negative energy states was because they were already full. He postulated that the entire Universe was filled with a "sea" of negative energy electrons, which remained generally invisible because of their universality. However, the sea would become visible in a sense if two gamma ray photons collided, producing enough energy to pop one of these negative-energy electrons to a positive energy level, becoming an ordinary familiar electron. It would leave behind a "hole" in the negative energy sea. The absence of a negatively-charged electron with negative energy, as Dirac saw it, would appear as a positively-charged particle with positive energy.
The process could run in reverse. An electron could fall back into this hole, or equivalently an electron could encounter this positively-charged "mirror" particle, with both particles disappearing and producing gamma rays.
Dirac was generally regarded as somewhat off the beaten path at best, being notorious for his uncommunicativeness. As he reported it, his personality was partly due to his upbringing in a house run by an extremely imperious and domineering father, an atmosphere where the lad learned to keep his mouth shut. Some suspect he exaggerated his problems with his father and was actually just autistic. In any case, it was said with only slight exaggeration that Dirac's vocabulary consisted only of "yes", "no", and "I don't know", and he didn't overuse them by any means. Reporters trying to interview him would always find the exercise painful:
"Do you go to the movies?"
"Yes."
Long pause. "When?"
"In 1920, perhaps also in 1930."
Dirac didn't find the exercise any more pleasant, and he tried to avoid reporters. When he learned he had been awarded the Nobel prize, he thought of declining it, until a colleague said that would attract much more attention to him than would accepting it. Incidentally, he only invited his mother to the ceremony.
Those who knew Dirac had many stories about his idiosyncrasies. If asked to clarify a point in a lecture, he would simply repeat what he had originally said, that being phrased in as perfect a fashion as possible to begin with. The British astrophysicist Fred Hoyle said that Dirac was reluctant to talk about a problem unless he had obtained the perfect solution for it, which made discussions difficult. Hoyle once called Dirac on the phone to ask if he would give a seminar, and the response was pure Dirac: "I will put the telephone down for a minute and think, and then speak again."
Dirac was still recognized as a genius and few dismissed his notion of a sea of negative-energy electrons out of hand. Reactions to the theory were still not universally positive. Niels Bohr suggested that the theory would make an excellent elephant trap. The elephant, Bohr commented, was a famously wise beast; if a copy of Dirac's theory was pinned up on a tree in the jungle someplace and an elephant happened to read it, the poor creature would be so mesmerized trying to figure it out that he could be captured and shipped to the Copenhagen zoo before he was any the wiser.
Dirac himself was not entirely sure what to make of his own ideas. A superficial consideration of the theory suggested that the particle had the same mass as the electron and a positive charge, but since nothing like that was known, he could only suggest that it was the proton. This seemed implausible and there were those who knew Dirac who suspected that it was his idea of a joke -- an implausible notion since few could see a trace of humor in him, and he later admitted that his motives were "sheer cowardice."
In any case, a German mathematician named Hermann Weyl (1885:1955) quickly performed an analysis that showed the positively-charged particle would indeed have to be the same mass as the electron, and in 1931 Dirac conceded that the hole would be effectively a positively charged "mirror" electron or "antielectron". In modern terms, collisions between gamma rays could result in the creation of an electron-antielectron "pair". Such "pair production" could also run in reverse, with an electron and antielectron "annihilating" each other completely, producing gamma rays.
Dirac then suggested that the proton had a negatively-charged equivalent, the "antiproton", and in general that all matter was mirrored by "antimatter" with reversed charge polarities. Antimatter would appear almost completely like normal matter, but if it came into contact with normal matter, the two would annihilate each other in a tremendous burst of energy produced by complete mass-energy conversion.
Incidentally, in 1933, the American physicist Robert Oppenheimer (1904:1967) and his colleague Wendell Furry published a reconsideration of Dirac's theory, validating his work while introducing a modified notation that discarded the concept of a universal sea of negative-energy electrons as so much excess baggage -- much to everybody's relief.
