29.3 Radioactivity 94529.3 RADIOACTIVITYIn 1896, Becquerel accidentally discovered that uranium salt crystals emit an invisibleradiation that can darken a photographic plate even if the plate is covered toexclude light. After several such observations under controlled conditions, he concludedthat the radiation emitted by the crystals was of a new type, one requiringno external stimulation. This spontaneous emission of radiation was soon calledradioactivity. Subsequent experiments by other scientists showed that othersubstances were also radioactive.The most significant investigations of this type were conducted by Marieand Pierre Curie. After several years of careful and laborious chemicalseparation processes on tons of pitchblende, a radioactive ore, the Curiesreported the discovery of two previously unknown elements, both of whichwere radioactive. These were named polonium and radium. Subsequent experiments,including Rutherford’s famous work on alpha-particle scattering,suggested that radioactivity was the result of the decay, or disintegration, of unstablenuclei.Three types of radiation can be emitted by a radioactive substance: alpha ()4particles, in which the emitted particles are 2 He nuclei; beta () particles, in whichand with Becquerel for their studies ofradioactive substances. In 1911 she wasMARIE CURIE, Polish Scientist(1867 – 1934)In 1903 Marie Curie shared the NobelPrize in physics with her husband, Pierre,the emitted particles are either electrons or positrons; and gamma () rays, inwhich the emitted “rays” are high-energy photons. A positron is a particle similarto the electron in all respects, except that it has a charge of e. (The positron issaid to be the antiparticle of the electron.) The symbol e is used to designate anawarded a second Nobel Prize in chemistryfor the discovery of radium and polonium.Marie Curie died of leukemia causedby years of exposure to radioactive substances.“I persist in believing that theelectron, and e designates a positron.ideas that then guided us are the onlyIt’s possible to distinguish these three forms of radiation by using the schemeones which can lead to the true socialdescribed in Figure 29.5. The radiation from a radioactive sample is directed intoprogress. We cannot hope to build a bettera region with a magnetic field, and the beam splits into three components, two world without improving the individual.bending in opposite directions and the third not changing direction. From this Toward this end, each of us must worksimple observation it can be concluded that the radiation of the undeflected beam toward his own highest development,(the gamma ray) carries no charge, the component deflected upward containspositively charged particles (alpha particles), and the component deflected downwardcontains negatively charged particles (e ). If the beam includes a positronaccepting at the same time his share ofresponsibility in the general life ofhumanity.”(e ), it is deflected upward.The three types of radiation have quite different penetrating powers. Alphaparticles barely penetrate a sheet of paper, beta particles can penetrate a fewmillimeters of aluminum, and gamma rays can penetrate several centimeters oflead. arrayThe Decay Constant and Half-LifeObservation has shown that if a radioactive sample contains N radioactive nuclei atsome instant, then the number of nuclei, N, that decay in a small time interval tis proportional to N ; mathematically,NNtorN N t [29.2]where is a constant called the decay constant. The negative sign signifies that Ndecreases with time; that is, N is negative. The value of for any isotope determinesthe rate at which that isotope will decay. The decay rate, or activity R, of asample is defined as the number of decays per second. From Equation 29.2, we seethat the decay rate isR Nt NIsotopes with a large value decay rapidly; those with small decay slowly.[29.3]FPG InternationalLeadRadioactivesourceDetector e– B inFigure 29.5 The radiation from aradioactive source, such as radium,can be separated into three componentsusing a magnetic field to deflectthe charged particles. The detectorarray at the right records theevents. The gamma ray isn’t deflectedby the magnetic field. Decay rate
946 Chapter 29 Nuclear <strong>Physics</strong>A general decay curve for a radioactive sample is shown in Active Figure 29.6. Itcan be shown from Equation 29.2 (using calculus) that the number of nuclei presentvaries with time according to the equationThe hands and numbers of this luminouswatch contain minute amountsof radium salt. The radioactive decayof radium causes the phosphors toglow in the dark.N 012 N 014 N 0N(t)T 1/2N =N 0 e – t2T 1/2ACTIVE FIGURE 29.6Plot of the exponential decay law forradioactive nuclei. The vertical axisrepresents the number of radioactivenuclei present at any time t, and thehorizontal axis is time. The parameterT 1/2 is the half-life of the sample.Log into <strong>Physics</strong>Now at www.cp7e.comand go to Active Figure 29.6, whereyou can observe the decay curves fornuclei with varying half-lives.TIP 29.2 Two Half-Lives Don’tMake a Whole-LifeA half-life is the time it takes for halfof a given number of nuclei to decay.During a second half-life, half theremaining nuclei decay, so in twohalf-lives, three-quarters of theoriginal material has decayed,not all of it.t© Richard Megna/Fundamental PhotographsN N 0 e t[29.4a]where N is the number of radioactive nuclei present at time t, N 0 is the numberpresent at time t 0, and e 2.718 . . . is Euler’s constant. Processes that obeyEquation 29.4a are sometimes said to undergo exponential decay. 1Another parameter that is useful for characterizing radioactive decay is the halflifeT 1/2 . The half-life of a radioactive substance is the time it takes for half of agiven number of radioactive nuclei to decay. Using the concept of half-life, it canbe shown that Equation 29.4a can also be written asN N 0 1 2 n[29.4b]where n is the number of half-lives. The number n can take any non-negative valueand need not be an integer. From the definition, it follows that n is related to timet and the half-life T 1/2 byn Setting N N 0 /2 and t T 1/2 in Equation 29.4a givesN 02 N 0e T 1/2[29.4c]Writing this in the form eT 1/2 2 and taking the natural logarithm of both sides,we getT 1/2 ln 2 0.693[29.5]This is a convenient expression relating the half-life to the decay constant. Notethat after an elapsed time of one half-life, N 0 /2 radioactive nuclei remain (by definition);after two half-lives, half of these will have decayed and N 0 /4 radioactivenuclei will be left; after three half-lives, N 0 /8 will be left; and so on.The unit of activity R is the curie (Ci), defined as1 Ci 3.7 10 10 decays/s[29.6]This unit was selected as the original activity unit because it is the approximateactivity of 1 g of radium. The SI unit of activity is the becquerel (Bq):1Bq 1 decay/s [29.7]Therefore, 1 Ci 3.7 10 10 Bq. The most commonly used units of activity are themillicurie (10 3 Ci) and the microcurie (10 6 Ci).Quick Quiz 29.1tT 1/2What fraction of a radioactive sample has decayed after two half-lives have elapsed?(a) 1/4 (b) 1/2 (c) 3/4 (d) not enough information to sayQuick Quiz 29.2Suppose the decay constant of radioactive substance A is twice the decay constant ofradioactive substance B. If substance B has a half life of 4 hr, what’s the half life ofsubstance A? (a) 8 hr (b) 4 hr (c) 2 hr (d) not enough information to say1 Other examples of exponential decay were discussed in Chapter 18 in connection with RC circuits and in Chapter 20in connection with RL circuits.
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876 Chapter 27 Quantum PhysicsSolve
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30.14 Electroweak Theory and the St
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30.15 The Cosmic Connection 999prot
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Problems 100330.12 Quarks &30.13 Co
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Problems 1005particles fuse to prod
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Problems 100740. Assume binding ene
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A.1 MATHEMATICAL NOTATIONMany mathe
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A.3 Algebra A.3by 8, we have8x8 32
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APPENDIX BAn Abbreviated Table of I
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An Abbreviated Table of Isotopes A.
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An Abbreviated Table of Isotopes A.
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Some Useful Tables A.15TABLE C.3The
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IndexPage numbers followed by “f
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Current, 568-573, 586direction of,
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Index I.5Fissionnuclear, 973-976, 9
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Polarizer, 805-806, 805f, 806-807Po
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South poleEarth’s geographic, 626
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CreditsPhotographsThis page constit
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PEDAGOGICAL USE OF COLORDisplacemen
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PHYSICAL CONSTANTSQuantity Symbol V