Quantum Physics

29.4 The Decay Processes 949Alpha DecayIf a nucleus emits an alpha particle ( 4 2He), it loses two protons and two neutrons.Therefore, the neutron number N of a single nucleus decreases by 2, Z decreasesby 2, and A decreases by 4. The decay can be written symbolically asAZ X : Z2 A4 Y 4 2 He[29.8]where X is called the parent nucleus and Y is known as the daughter nucleus. Asexamples, 238 U and 226 Ra are both alpha emitters and decay according to theschemes23892 U : 23490 Th 4 2 He[29.9]and22688 Ra : 22286 Rn 4 2 He[29.10]The half-life for 238 U decay is 4.47 10 9 years, and the half-life for 226 Ra decay is1.60 10 3 years. In both cases, note that the A of the daughter nucleus is four lessthan that of the parent nucleus, while Z is reduced by two. The differences are accountedfor in the emitted alpha particle (the 4 He nucleus).The decay of 226 Ra is shown in Active Figure 29.7. When one element changesinto another, as happens in alpha decay, the process is called spontaneous decay ortransmutation. As a general rule, (1) the sum of the mass numbers A must be thesame on both sides of the equation, and (2) the sum of the atomic numbers Zmust be the same on both sides of the equation.In order for alpha emission to occur, the mass of the parent must be greaterthan the combined mass of the daughter and the alpha particle. In thedecay process, this excess mass is converted into energy of other forms andappears in the form of kinetic energy in the daughter nucleus and the alphaparticle. Most of the kinetic energy is carried away by the alpha particle becauseit is much less massive than the daughter nucleus. This can be understoodby first noting that a particle’s kinetic energy and momentum p are related asfollows:pRnBefore decayKE Rn226 Ra88222 Rn86After decayKE Ra = 0p Ra = 0KEααp αACTIVE FIGURE 29.7The alpha decay of radium-226. Theradium nucleus is initially at rest. Afterthe decay, the radon nucleus haskinetic energy KE Rn and momentump: Rn , and the alpha particle has kineticenergy KE and momentum .p: Log into PhysicsNow at www.cp7e.comand go to Active Figure 29.7, whereyou can observe the decay ofradium-226.KE p22mBecause momentum is conserved, the two particles emitted in the decay of anucleus at rest must have equal, but oppositely directed, momenta. As a result, thelighter particle, with the smaller mass in the denominator, has more kinetic energythan the more massive particle.Quick Quiz 29.3If a nucleus such as 226 Ra that is initially at rest undergoes alpha decay, which ofthe following statements is true? (a) The alpha particle has more kinetic energythan the daughter nucleus. (b) The daughter nucleus has more kinetic energythan the alpha particle. (c) The daughter nucleus and the alpha particle have thesame kinetic energy.Applying Physics 29.2Energy and Half-lifeIn comparing alpha decay energies from a number ofradioactive nuclides, why is it found that the half-life ofthe decay goes down as the energy of the decay goes up?Explanation It should seem reasonable that thehigher the energy of the alpha particle, the morelikely it is to escape the confines of the nucleus.The higher probability of escape translates to afaster rate of decay, which appears as a shorterhalf-life.