Atomic nuclei are composed of two types of particles, protons and neutrons, which are collectively known as nucleons. A proton is simply the nucleus of an ordinary hydrogen atom, the lightest atom, and has a unit positive charge. A neutron is an uncharged particle of about the same mass as the proton. The number of protons in a given nucleus is the atomic number of that nucleus and determines which chemical element the nucleus will constitute when surrounded by electrons.
The total number of protons and neutrons together in a nucleus is the atomic mass number of the nucleus. Two nuclei may have the same atomic number but different mass numbers, thus constituting different forms, or isotopes, of the same element. The mass number of a given isotope is the nearest whole number to the atomic weight of that isotope and is approximately equal to the atomic weight (in the case of carbon-12, exactly equal).Size and Density
The nucleus occupies only a tiny fraction of the volume of an atom (the radius of the nucleus being some 10,000 to 100,000 times smaller than the radius of the atom as a whole), but it contains almost all the mass. An idea of the extreme density of the nucleus is revealed by a simple calculation. The radius of the nucleus of hydrogen is on the order of 10-13 cm so that its volume is on the order of 10-39 cm3 (cubic centimeter); its mass is about 10-24 g (gram). Combining these to estimate the density, we have 10-24 g/10-39 cm3 ≈ 1015 g/cm3, or about a thousand trillion times the density of matter at ordinary scales (the density of water is 1 g/cm3).Mass Defect, Binding Energy, and Nuclear Reactions
When nuclear masses are measured, the mass is always found to be less than the sum of the masses of the individual nucleons bound in the nucleus. The difference between the nuclear mass and the sum of the individual masses is known as the mass defect and is due to the fact that some of the mass must be converted to energy in order to make the nucleus stable. This nuclear binding energy is related to the mass defect by the famous formula from relativity, E = mc2, where E is energy, m is mass, and c is the speed of light. The binding energy of a nucleus increases with increasing mass number.
A more interesting property of a nucleus is the binding energy per nucleon, found by dividing the binding energy by the mass number. The average binding energy per nucleon is observed to increase rapidly with increasing mass number up to a mass number of about 60, then to decrease rather slowly with higher mass numbers. Thus, nuclei with mass numbers around 60 are the most stable, and those of very small or very large mass numbers are the least stable.
Two important phenomena result from this property of nuclei. Nuclear fission is the spontaneous splitting of a nucleus of large mass number into two nearly equal nuclei whose mass numbers are in the most stable range. Nuclear fusion, on the other hand, is the combining of two light nuclei to form a heavier single nucleus, again with an increase in the average binding energy per nucleon. In both cases, the change to a more stable final state is accompanied by the release of a large amount of energy per unit mass of the reacting materials as compared to the energy released in chemical reactions (see nuclear energy).
Several models of the nucleus have evolved that fit certain aspects of nuclear behavior, but no single model has successfully described all aspects. One model is based on the fact that certain properties of a nucleus are similar to those of a drop of incompressible liquid. The liquid-drop model has been particularly successful in explaining details of the fission process and in evolving a formula for the mass of a particular nucleus as a function of its atomic number and mass number, the so-called semiempirical mass formula.
Another model is the Fermi gas model, which treats the nucleons as if they were particles of a gas restricted by the Pauli exclusion principle, which allows only two particles of opposite spin to occupy a particular energy level described by the quantum theory. These particle pairs will fill the lowest energy levels first, then successively higher ones, so that the "gas" is one of minimum energy. There are actually two independent Fermi gases, one of protons and one of neutrons. The tendency of nucleons to occupy the lowest possible energy level explains why there is a tendency for the numbers of protons and neutrons to be nearly equal in lighter nuclei. In heavier nuclei the effect of electrostatic repulsion among the larger number of charges from the protons raises the energy of the protons, with the result that there are more neutrons than protons (for uranium-235, for example, there are 143 neutrons and only 92 protons). The pairing of nucleons in energy levels also helps to explain the tendency of nuclei to have even numbers of both protons and neutrons.
Neither the liquid-drop model nor the Fermi gas model, however, can explain the exceptional stability of nuclei having certain values for either the number of protons or the number of neutrons, or both. These so-called magic numbers are 2, 8, 20, 28, 50, 82, and 126. Because of the similarity between this phenomenon and the stability of the noble gases, which have certain numbers of electrons that are bound in closed "shells," a shell model was suggested for the nucleus. There are major differences, however, between the electrons in an atom and the nucleons in a nucleus. First, the nucleus provides a force center for the electrons of an atom, while the nucleus itself has no single force center. Second, there are two different types of nucleons. Third, the assumption of independent particle motion made in the case of electrons is not as easily made for nucleons. The liquid-drop model is in fact based on the assumption of strong forces between the nucleons that considerably constrain their motion. However, these difficulties were solved and a good explanation of the magic numbers achieved on the basis of the shell model, which included the assumption of strong coupling between the spin angular momentum of a nucleon and its orbital angular momentum. Various attempts have been made, with partial success, to construct a model incorporating the best features of both the liquid-drop model and the shell model.
A nucleus may be represented conveniently by the chemical symbol for the element together with a subscript and superscript for the atomic number and mass number. (The subscript is often omitted, since the element symbol fixes the atomic number.) The nucleus of ordinary hydrogen, i.e., the proton, is represented by 1H1, an alpha particle (a helium nucleus) is 2He4, the most common isotope of chlorine is 17Cl35, and the uranium isotope used in the atomic bomb is 92U235.
Nuclear reactions involving changes in atomic number or mass number can be expressed easily using this notation. For example, when Ernest Rutherford produced the first artificial nuclear reaction (1919), it involved bombarding a nitrogen nucleus with alpha particles and resulted in an isotope of oxygen with the release of a proton: 2He4+7N14→8O17+1H1. Note that the total of the atomic numbers on the left is equal to the total on the right (i.e., 2+7=8+1), and similarly for the mass numbers (4+14=17+1).
Following the discovery of radioactivity by A. H. Becquerel in 1896, Ernest Rutherford identified two types of radiation given off by natural radioactive substances and named them alpha and beta; a third, gamma, was later identified. In 1911 he bombarded a thin target of gold foil with alpha rays (subsequently identified as helium nuclei) and found that, although most of the alpha particles passed directly through the foil, a few were deflected by large amounts. By a quantitative analysis of his experimental results, he was able to propose the existence of the nucleus and estimate its size and charge.
After the discovery of the neutron in 1932, physicists turned their attention to the understanding of the strong interactions, or strong nuclear force, that bind protons and neutrons together in nuclei. This force must be great enough to overcome the considerable repulsive force existing between several protons because of their electrical charge. It must exist between nucleons without regard to their charge, since it acts equally on protons and neutrons, and it must not extend very far away from the nucleons (i.e., it must be a short-range force), since it has negligible effect on protons or neutrons outside the nucleus.
In 1935 Hideki Yukawa proposed a theory that this nuclear "glue" was produced by the exchange of a particle between nucleons, just as the electromagnetic force is produced by the exchange of a photon between charged particles. The range of a force is dependent on the mass of the particle carrying the force; the greater the mass of the particle, the shorter the range of the force. The range of the electromagnetic force is infinite because the mass of the photon is zero. From the known range of the nuclear force, Yukawa estimated the mass of the hypothetical carrier of the nuclear force to be about 200 times that of the electron. Given the name meson because its mass is between that of the electron and those of the nucleons, this particle was finally observed in 1947 and is now called the pi meson, or pion, to distinguish it from other mesons that have been discovered (see elementary particles).
Both the proton and the neutron are surrounded by a cloud of pions given off and reabsorbed again within an incredibly short interval of time. Certain other mesons are assumed to be created and destroyed in this way as well, all such particles being termed "virtual" because they exist in violation of the law of conservation of energy (see conservation laws) for a very short span of time allowed by the uncertainty principle. It is now known, however, that at a more fundamental level the actual carrier of the strong force is a particle called the gluon.
See G. Gamow, The Atom and Its Nucleus (1961); R. K. Adair, The Great Design: Particles, Fields, and Creation (1987).