Quantum Physics

29.4 The Decay Processes 951Strategy As in preceding problems, finding the released energy involves computing the difference in massbetween the resultant particle(s) and the initial particle(s) and converting to MeV.Solution14 14Obtain the masses of 6 C and 7N from Appendix B and m m C m N 14.003 242 u 14.003 074 u 0.000 168 ucompute the difference between them:Convert the mass difference to MeV:E (0.000 168 u)(931.494 MeV/u) 0.156 MeVRemarks The calculated energy is generally more than the energy observed in this process. The discrepancy led toa crisis in physics, because it appeared that energy wasn’t conserved. As discussed below, this crisis was resolved by thediscovery that another particle was also produced in the reaction.Exercise 29.640Calculate the maximum energy liberated in the beta decay of radioactive potassium to calcium: 19 K : 4020 Ca .Answer1.31 MeVFrom Example 29.6, we see that the energy released in the beta decay of 14 C isapproximately 0.16 MeV. As with alpha decay, we expect the electron to carry awayvirtually all of this energy as kinetic energy because, apparently, it is the lightestparticle produced in the decay. As Figure 29.8 shows, however, only a small numberof electrons have this maximum kinetic energy, represented as KE max on thegraph; most of the electrons emitted have kinetic energies lower than that predictedvalue. If the daughter nucleus and the electron aren’t carrying away this liberatedenergy, then where has the energy gone? As an additional complication,further analysis of beta decay shows that the principles of conservation of bothangular momentum and linear momentum appear to have been violated!In 1930 Pauli proposed that a third particle must be present to carry away the“missing” energy and to conserve momentum. Later, Enrico Fermi developed acomplete theory of beta decay and named this particle the neutrino (“little neutralone”) because it had to be electrically neutral and have little or no mass. Althoughit eluded detection for many years, the neutrino () was finally detected experimentallyin 1956. The neutrino has the following properties:• Zero electric charge• A mass much smaller than that of the electron, but probably not zero. (Recentexperiments suggest that the neutrino definitely has mass, but the value isuncertain—perhaps less than 1 eV/c 2 .)1• A spin of2• Very weak interaction with matter, making it difficult to detectWith the introduction of the neutrino, we can now represent the beta decayprocess of Equation 29.13 in its correct form:146 C : 14 7 N e [29.15]The bar in the symbol indicates an antineutrino. To explain what an antineutrinois, we first consider the following decay:127N : 12 6 C e [29.16] Properties of the neutrinoTIP 29.3 Mass Number of theElectronAnother notation that is sometimes0used for an electron is 1 e . Thisnotation does not imply that theelectron has zero rest energy. Themass of the electron is much smallerthan that of the lightest nucleon, sowe can approximate it as zero whenwe study nuclear decays andreactions.Number of -particlesKinetic energy(a)K maxNumber of -particlesKinetic energy(b)Figure 29.8 (a) Distribution ofbeta particle energies in a typical betadecay. All energies are observed up toa maximum value. (b) In contrast,the energies of alpha particles froman alpha decay are discrete.