Quantum Physics

966 Chapter 29 Nuclear Physicswhere A is the mass number and r 0 is a constant equal Note that in this decay, as in all radioactive decayto 1.2 10 15 m.processes, the sum of the Z values on the left equals theThe total mass of a nucleus is always less than the sum sum of the Z values on the right; the same is true for theof the masses of its individual nucleons. This mass differencem, multiplied by c 2 , gives the binding energy of A typical beta decay isA values.the nucleus.146 C : 14 7 N e [29.15]When a nucleus undergoes beta decay, an antineutrino29.3 Radioactivityis emitted along with an electron, or a neutrino alongThe spontaneous emission of radiation by certain nuclei with a positron. A neutrino has zero electric charge andis called radioactivity. There are three processes by a small mass (which may be zero) and interacts weaklywhich a radioactive substance can decay: alpha () decay, with matter.4in which the emitted particles are 2 He nuclei; beta () Nuclei are often in an excited state following radioactivedecay, and they release their extra energy by emit-decay, in which the emitted particles are electrons orpositrons; and gamma () decay, in which the emitted ting a high-energy photon called a gamma ray (). Aparticles are high-energy photons.typical gamma ray emission isThe decay rate, or activity, R, of a sample is given by126 C * : 12 6 C [29.18]R Nt N[29.3]where N is the number of radioactive nuclei at some instantand is a constant for a given substance called thedecay constant.Nuclei in a radioactive substance decay in such a waythat the number of nuclei present varies with time accordingto the expressionwhere the asterisk indicates that the carbon nucleus wasin an excited state before gamma emission.29.6 Nuclear ReactionsNuclear reactions can occur when a bombarding particlestrikes another nucleus. A typical nuclear reaction isN N 0 e t[29.4a]42 He 14 7 N : 17 8O 1 1 H[29.21]where N is the number of radioactive nuclei present attime t, N 0 is the number at time t 0, and e 2.718 . . . isthe base of the natural logarithms.The half-life T 1/2 of a radioactive substance is thetime required for half of a given number of radioactivenuclei to decay. The half-life is related to the decay constantbyT 1/2 0.693[29.5]In this reaction, an alpha particle strikes a nitrogen nucleus,producing an oxygen nucleus and a proton. As inradioactive decay, atomic numbers and mass numbersbalance on the two sides of the arrow.Nuclear reactions in which energy is released are saidto be exothermic reactions and are characterized bypositive Q values. Reactions with negative Q values,called endothermic reactions, cannot occur unless theincoming particle has at least enough kinetic energy toovercome the energy deficit. In order to conserve bothenergy and momentum, the incoming particle musthave a minimum kinetic energy, called the thresholdenergy, given by29.4 The Decay ProcessesIf a nucleus decays by alpha emission, it loses two protonsand two neutrons. A typical alpha decay is23892 U : 23490 Th 4 2 He[29.9]KE min 1 m M Q[29.24]where m is the mass of the incident particle and M is themass of the target atom.