by Brad Lambert
A Brief History of the Atom
For over two thousand years, humans have had a notion that matter was only divisible to a certain point, beyond which a sample of a specific type of matter would cease to display its characteristics. The early Greeks called these smallest units "atomos", which means "indivisible". Almost two thousand years later, we have adopted the name "atoms" from the ancient Greeks to describe these tiny bases of matter. (Webster 113)
The representation of atoms has changed over the course of history, though. Atoms were first thought to be little spheres that simply could not be divided. Then, as more scientists accepted the theory of atoms, the model changed a bit to include a ball of positive charge with little negative charges stuck throughout. This "plum pudding" model held from the 1890's until 1911. It was then that Ernest Rutherford performed an experiment that uncovered evidence that seemed to contradict the plum pudding model of an atom. By directing a beam of alpha particles, later known to be bare helium nuclei, at a thin sheet of gold foil, Rutherford expected to see the alpha particles only slightly deflected. He reasoned that since the mass of the alpha particle was much greater than that of the electron, and there should be no great concentration of positive charge, the alpha particles should travel through the foil virtually undeflected. He found, however, that some of the alpha particles were deflected at a much larger than expected angle; in fact, some of the particles came back almost head-on with the alpha particle source. These observations led Rutherford to formulate his own theory of the atomic structure. He postulated that the atom was comprised of a small sphere of positive charge, called the nucleus, and orbiting the nucleus were the negatively charged electrons. This "planetary model" seemed to make sense, but it had two problems. First, it suggested that light of any frequency could be emitted from an atom; experiment showed that only certain frequencies were given off by certain atoms by a phenomenon known as line spectra. Also, the planetary model suggested that all matter should be unstable; the electrons should quickly spiral into the nucleus, but everyday observations showed that this clearly was not the case. A Danish physicist, Niels Bohr, thought that the Rutherford model had promise, but Bohr felt that the new quantum theory could explain the discrepancies between predicted and actual results. By allowing electrons only certain energy values while orbiting the nucleus, Bohr could explain atomic line spectra and accurately predict the frequencies of the line spectra of hydrogen. Though it has since proven inaccurate for atoms other than hydrogen, Bohr's theory is still used today to simplify beginning courses on the atom. (Giancoli 731-739)
Properties of the Nucleus
Structure
Just what is this nucleus made of? It's already been stated that the nucleus is positively charged and has no electrons in it, but is the nucleus one big ball of charge that varies from element to element? It turns out that no, the nucleus is made of structures known as protons and neutrons. Protons have the same charge as electrons, only positive. Neutrons, as their name would suggest, are neutral particles. Neutrons lack the charge protons have, but their mass is about the same as protons (neutrons are actually slightly more massive). (Ohanian 20)
If neutrons were electrically neutral, and only charged particles could be controlled with a magnetic field, how did physicists discover the neutron? James Chadwick found that bombarding beryllium with alpha particles created a new type of radiation that, when directed toward paraffin, dislodged protons and also gave heavier atoms energy, though not nearly as much as they gave the protons of hydrogen. The protons dislodged left the paraffin wax with great velocities. At first, scientists postulated that the radiation was electromagnetic, but the high kinetic energy suggested that if the source were electromagnetic, the energy given off from the beryllium nucleus would have to be ten times that of the kinetic energy of the incident alpha particles. Either the law of conservation of energy was being violated, or the radiation was some new particle. After more closely studying the recoils of atoms other than hydrogen, Chadwick found that a pattern showed that was consistent with the notion that the particle had a mass comparable to that of a proton. To explain their great penetrability, the particles would have to be electrically neutral, as a charged particle would react with the electric fields inside the atom. Chadwick performed several experiments and calculated the mass of the particle, and in 1932, he announced the existence of the new particle he deemed the neutron. (Weinberg 144-147)
One peculiar formation of the nucleus is a rare and little-understood phenomenon known as a nuclear halo. The most common example is lithium-11 (11L). In the formation of halos, several neutrons or protons leave the nucleus and orbit it, much like electrons orbit nuclei. In 11L, two of the nuclear neutrons leave the nucleus and form a halo that surrounds the nucleus, leaving a structure that acts like 9L and two neutrons. Experiments show, though, that interaction with one of the halo neutrons will cause the other to be displaced, as well. These halo neutrons were found to be held to the nucleus at a distance of about 5 * 10-15 m, or about twice the radius of a nucleus with 11 nucleons, and at energies of less than one MeV. This makes it easy to strip the 11L nucleus of the two neutrons, making 9L. This easy stripping of the nucleus makes halo formations fairly easy to detect, but as of yet, not much is known about the value or importance of this phenomenon. (Austin and Bertsch 1-2)
Forces involved
In the nucleus, there are two forces involved. The Coulomb, or electromagnetic, force acts on the protons in the nucleus. Since all the protons have the same charge, logic would seem to say that the nucleus should fly apart due to the tremendous electric repulsion. However, there exists a second force in the nucleus known as the strong nuclear force. The strong nuclear force is much stronger than the electromagnetic force, and therefore can overpower the Coulomb repulsion and hold protons together. However, unlike the electromagnetic force, the strong nuclear force has a limit to its range, on the order of 10-15 m. If one could force the protons to move farther apart than this limit, the electromagnetic force would take over and cause the protons to repel each other and fly apart. (Calder 16) This will be examined a bit more in detail later.
The point was made earlier that nuclei do not contain electrons, and that experiment seemed to prove this, but why is this so? To answer this, we need to use a form of Werner Heisenberg's uncertainty principle. The uncertainty principle states that we can never know precisely the momentum or position of a particle. Specifically, the equation of interest here is
[[Delta]]p[[Delta]]x >= h/4[[pi]]
where [[Delta]]p is the uncertainty in momentum, [[Delta]]x is the uncertainty in position, and h is Planck's constant, 6.626 * 10-34 J*s. (Beiser 109) Taking the value of [[Delta]]x to be the typical nuclear size, about 5 * 10-15 m, the corresponding value of [[Delta]]p would be 1.1 * 10-20 kg*m/s. A momentum of this magnitude would give the electron relativistic energy -- on the order of 20 MeV. This is in contradiction with experiment and observation; observed beta-decay energies are on the order of 2 to 3 MeV. However, putting the same conditions on the proton yields a kinetic energy of just .23 MeV, which is feasible for nucleon kinetic energy. (Beiser 409)
Nuclear Interactions
Radioactivity
There are several known interactions that change the nucleus. For this section, only those reactions that help a nucleus achieve stability will be considered. The main types of radioactive decay in the nucleus are alpha, beta, and gamma emissions. Alpha particles are 4He nuclei stripped of their electrons. These particles, because of their +2 charge, are not very penetrating. Beta particles are electrons, and sometimes positrons (the antiparticles of electrons), formed in and ejected from the nucleus. Beta particles are somewhat more penetrating than alpha particles, though 3 mm of aluminum will stop beta particles. Gamma rays are highly energetic electromagnetic waves. These rays are the most penetrating type of radiation; Pb of several centimeters' thickness is not sufficient to stop them. (Giancoli 806)
Upon first inspection, alpha decay seems to make perfect sense. An atom that has too many nucleons in the nucleus can simply reduce this number by ejecting an alpha particle, thereby reducing the atomic number by two and the atomic weight by four. Upon closer inspection, however, a problem arises with the classical view of alpha decay. Observed kinetic energies of alpha particles in decays are in the range of about 4 to 9 MeV, but the potential barrier of a typical nucleus is about 25 MeV, which means that, assuming that the alpha particle has the same kinetic energy inside the atom as outside, the alpha particle should have no chance for escape from the nucleus. Quantum mechanics, however, allows for a phenomenon known as tunneling, which would give the alpha particle a chance of penetrating the energy barrier, even if its energy were lower than that of the barrier. This chance is small, though; typical alpha particles collide with the barrier about 1021 times per second, and still must wait many years, occasionally billions of years, to escape. To illustrate an example in the macroscopic world, a person walking out of a room has a chance of leaving the room by passing straight through the closed door, but this chance is so incredibly small that we never observe such a phenomenon. On the microscopic level, though, energies and masses are much smaller, allowing for such an event to occur with more frequency. (Beiser 461-463)
Beta decay is in some ways similar to alpha decay, but in others, the two are completely different. In beta decay, one of two things happen. Either a neutron breaks down into a proton and an electron which is emitted from the nucleus, or a proton converts into a neutron and a positron which is emitted. In both cases, problems arise. First, the electron or positron emitted carries off much less kinetic energy than it should. Also, neither equation conserves spin, a measure of angular momentum. The neutron, the proton, the electron, and the positron all have spins of 1/2. To resolve these problems, a new particle was introduced that would also have spin 1/2. This new particle would have to be electrically neutral to keep charge conserved, and would carry off the majority of the kinetic energy. Enrico Fermi called it the "neutrino", or "little neutral one". In 1953, scientists confirmed the existence of this particle, and the beta reactions were rewritten as
n -> p+ + e- + [[nu]]
and
p+ -> n + e- + [[nu]]
where [[nu]] is a neutrino and [[nu]] is its antiparticle, the antineutrino. (Beiser 467-469)
Gamma rays are the most penetrating, but the easiest to explain. A nucleus is capable of being in an excited state, like electrons orbiting in an atom, and when the nucleus returns to its ground state, a photon is given off. With electrons, the photon is one of X-rays, on the order of several eV, sometimes a few keV. With nucleons, however, the photon released is a gamma ray, and the energy is on the order of keV or MeV. There is no change to the nuclear structure, only an intense release of energy. (Giancoli 810-811)
Fission and Fusion
Two reactions of nuclei liberate huge amounts of energy. These reactions are fission and fusion of nuclei. In fission, neutrons strike a heavy nucleus and cause the nucleus to split into two daughter nuclei of almost equal mass. Fusion brings two light nuclei together to form a heavier one. Per reaction, fission releases more energy than fusion; however, per unit mass of material, fusion liberates more energy than fission. For comparison, the average fission of 235U liberates ~200 MeV per reaction, whereas the most common fusion reaction produces ~17 MeV per reaction. However, completely fusing 1 kg of deuterium (2H) releases the same amount of energy as the fissioning of 1.07 kg of 235U. As of yet, we have learned to control the fission reaction, and we harness its power to produce electricity at power plants. Research is underway to see if we can control the fusion reaction and obtain enough energy to make fusion a feasible source of energy. Researchers project that by the year 2010, we will be able to achieve a self-sustaining fusion reaction in reactors under development. (Bourham)
Over the past century, mankind has made many advances in the theories about the nucleus of the atom. We still continue to learn every day about the properties and interactions of nuclei. The future is full of possibilities. We know so little of halo nuclei. What is their importance? Is it possible to cause this phenomenon artificially? If so, could we use it to our advantage? Also, the future of fusion lies ahead. We've built many different types of reactors to date, but none has been successful in achieving a self-sustaining reaction. How far away is that goal? When we do achieve it, the use of fusion for energy could solve many energy problems. Pioneers in the field continue to make the trek down the road to fusion, and to achieve the goal, the future needs what this generation has to offer. Many answers lie ahead, waiting to be discovered.
Works Cited
Austin, Sam M. and Bertsch, George F. "Halo Nuclei". Scientific American, June 1995,
vol. 272, no. 6.
Beiser, Arthur. Concepts of Modern Physics. McGraw Hill Book Company, 1987.
Bourham, Mohamed A. "Fusion in the 21st Century: Promises and Challenges". Lecture given at NC State University, 21 June 1995.
Calder, Nigel. The Key to the Universe. New York: The Viking Press, 1977.
Giancoli, Douglas C. Physics. Englewood Cliffs, NJ: Prentice Hall, 1991.
Ohanian, Hans C. Modern Physics. Englewood Cliffs, NJ: Prentice Hall, 1987.
Webster's Ninth New Collegiate Dictionary. Springfield, MA: Merriam-Webster Inc.,
1988.