Quantum Physics

942 Chapter 29 Nuclear Physics(b) Calculate the radius of the star, treating it as a giantatomic nucleus.Substitute into Equation 29.1: r r 0 A 1/3 (1.2 10 15 m)(1.79 10 57 ) 1/3 1.46 10 4 m(c) Calculate the density of the star, assuming that itsmass is distributed uniformly.Substitute values into the equation for density andassume the star is a uniform sphere: m V m43r 3 3.00 1030 kg43 (1.46 10 4 m) 3 2.30 10 17 kg/m 3Remarks This density is typical of atomic nuclei as well as of neutron stars. A ball of neutron star matter having aradius of only 1 meter would have a powerful gravity field: it could attract objects a kilometer away at an accelerationof over 50 m/s 2 !Exercise 29.1Estimate the radius of a uranium-235 nucleus.Answer7.41 10 15 mMARIA GOEPPERT-MAYER,German Physicist (1906 – 1972)Goeppert-Mayer was born and educatedin Germany. She is best known for herdevelopment of the shell model of thenucleus, published in 1950. A similarmodel was simultaneously developed byHans Jensen, a German scientist. MariaGoeppert-Mayer and Hans Jensen wereawarded the Nobel Prize in physics in 1963for their extraordinary work inunderstanding the structure of the nucleus.Courtesy of Louise Barker/AIP Niels Bohr LibraryNuclear StabilityGiven that the nucleus consists of a closely packed collection of protons andneutrons, you might be surprised that it can even exist. The very large repulsiveelectrostatic forces between protons should cause the nucleus to fly apart.However, nuclei are stable because of the presence of another, short-range(about 2 fm) force: the nuclear force, an attractive force that acts between allnuclear particles. The protons attract each other via the nuclear force, and at thesame time they repel each other through the Coulomb force. The attractivenuclear force also acts between pairs of neutrons and between neutrons andprotons.The nuclear attractive force is stronger than the Coulomb repulsive forcewithin the nucleus (at short ranges). If this were not the case, stable nucleiwould not exist. Moreover, the strong nuclear force is nearly independent ofcharge. In other words, the nuclear forces associated with proton–proton,proton–neutron, and neutron–neutron interactions are approximately thesame, apart from the additional repulsive Coulomb force for the proton–protoninteraction.There are about 260 stable nuclei; hundreds of others have been observed,but are unstable. A plot of N versus Z for a number of stable nuclei is given inFigure 29.3. Note that light nuclei are most stable if they contain equal numbers ofprotons and neutrons, so that N Z, but heavy nuclei are more stable if N Z.This difference can be partially understood by recognizing that as the number ofprotons increases, the strength of the Coulomb force increases, which tends tobreak the nucleus apart. As a result, more neutrons are needed to keep thenucleus stable, because neutrons are affected only by the attractive nuclearforces. In effect, the additional neutrons “dilute” the nuclear charge density. Eventually,when Z 83, the repulsive forces between protons cannot be compensatedfor by the addition of neutrons. Elements that contain more than 83 protons don’thave stable nuclei, but decay or disintegrate into other particles in variousamounts of time. The masses and some other properties of selected isotopes areprovided in Appendix B.