Mass. Particle Charge (C) Kilograms (kg) Units (u) Electron. Hydrogen atom

Transcription

1 oms consis of elecrons in orbi abou a cenral nucleus. s we have seen in Chaper 30, he elecron orbis are quanum mechanical in naure and have ineresing characerisics. Lile has been said abou he nucleus, however. Since he nucleus is ineresing in is own righ, we now consider i in greaer deail. The nucleus of an aom consiss of neurons and proons, collecively referred o as nucleons. The neuron, discovered in 1932 by he English physicis James Chadwick ( ), carries no elecric charge and has a mass slighly larger han ha of a proon (see Table 31.1). The number of proons in he nucleus is differen in differen elemens and is given by he aomic number Z. In an elecrically neural aom, he number of nuclear proons equals he number of elecrons in orbi around he nucleus. The number of neurons in he Mass Elecric omic Mass Paricle Charge (C) Kilograms (kg) Unis (u) Elecron Proon euron Hydrogen aom

2 nucleus is. The oal number of proons and neurons is referred o as he aomic mass number because he oal nuclear mass is approximaely equal o imes he mass of a single nucleon: Z (31.1) umber of proons and neurons (aomic mass number or nucleon number) umber of proons (aomic number) umber of neurons Someimes is also called he nucleon number. shorhand noaion is ofen used o specify Z and along wih he chemical symbol for he elemen. For insance, he nuclei of all naurally occurring aluminum aoms have 27, and he aomic number for aluminum is Z 13 l. The number of neurons in an aluminum nucleus is Z. In general, for an elemen whose chemical symbol is X, he symbol for he nucleus is Z X umber of proons and neurons umber of proons For a proon he symbol is 1 1 H, since he proon is he nucleus of a hydrogen aom. neuron is denoed by 0 1 n. In he case of an elecron we use 0 1e, where 0 because an elecron is no composed of proons or neurons and Z 1 because he elecron has a negaive charge. uclei ha conain he same number of proons, bu a differen number of neurons, are known as isoopes. Carbon, for example, occurs in naure in wo sable forms. In mos carbon aoms (98.90%), he nucleus is he 12 6C isoope and consiss of six proons and six neurons. small fracion (1.10%), however, conain nuclei ha have six proons and 13 seven neurons namely, he 6C isoope. The percenages given here are he naural abundances of he isoopes. The aomic masses in he periodic able are average aomic masses, aking ino accoun he abundances of he various isoopes. The proons and neurons in he nucleus are clusered ogeher o form an approximaely spherical region, as Figure 31.1 illusraes. Experimen shows ha he radius r of he nucleus depends on he aomic mass number and is given approximaely in meers by r ( m) 1/3 (31.2) The radius of he aluminum nucleus ( 27), for example, is r ( m)27 1/ m. Equaion 31.2 leads o an imporan conclusion concerning he nuclear densiy of differen aoms, as Concepual Example 1 discusses. The nucleus is approximaely spherical (radius r) and conains proons ( ) clusered closely ogeher wih neurons ( ). r I is well known ha lead and oxygen conain differen aoms and ha he densiy of solid lead Equaion 31.2, decide wheher he densiy of he nucleus in a lead aom is (a) greaer han, (b) approximaely equal o, or (c) less han he densiy of he nucleus in an oxygen aom. The densiy M divided by is volume V: M/V (Equaion 11.1). The mass of a nucleus is approximaely equal o he number of nucleons in he nucleus imes he mass m of a single nucleon, since he masses of a proon and a neuron are nearly he same. Thus, we have ha M m, where is greaer for lead han for oxygen, bu m is he same for boh. The nucleus is approximaely spherical wih 4 a radius r, so is volume V is given by V r 3 3. The radius, however, depends on he number of nucleons hrough he relaion r ( m) 1/3 (Equaion 31.2). Therefore, we can wrie he densiy of a nucleus as follows: M V m m m 4 3 r [( m) 1/3 ] ( m) 3

3 oe ha he nucleon number has been eliminaed algebraically from his resul, as a direc consequence of Equaion The resul obained in he Reasoning secion for he nuclear densiy depends only on numerical facors and he value of m, which is he mass of a single nucleon no maer where he nucleon is locaed. The nuclear densiy does no depend on he nuclear number. Thus, he nuclear densiy of lead, which is he raio of is mass o is volume, is neiher greaer han nor less han he nuclear densiy of oxygen. The resul obained in he Reasoning secion for he nuclear densiy indicaes ha he densiy of he nucleus in a lead aom is approximaely he same as i is in an oxygen aom. In general, because of Equaion 31.2, he nuclear densiy has nearly he same value in all aoms. The difference in densiies beween solid lead and gaseous oxygen, however, arises mainly because of he difference in how closely he aoms are packed ogeher in he solid and gaseous phases. Problem 9 Two posiive charges ha are as close ogeher as hey are in a nucleus repel one apar? Clearly, some kind of aracive force mus hold he nucleus ogeher, since many kinds of naurally occurring aoms conain sable nuclei. The graviaional force of aracion beween nucleons is oo weak o counerac he repulsive elecric force, so a differen ype of force mus hold he nucleus ogeher. This force is he srong nuclear force and is one of only hree fundamenal forces ha have been discovered, fundamenal in he sense ha all forces in naure can be explained in erms of hese hree. The graviaional force is also one of hese forces, as is he elecroweak force (see Secion 31.5). Many feaures of he srong nuclear force are well known. For example, i is almos independen of elecric charge. a given separaion disance, nearly he same nuclear force of aracion exiss beween wo proons, beween wo neurons, or beween a proon and a neuron. The range of acion of he srong nuclear force is exremely shor, wih he force of aracion being very srong when wo nucleons are as close as m and essenially zero a larger disances. In conras, he elecric force beween wo proons decreases o zero only gradually as he separaion disance increases o large values and, herefore, has a relaively long range of acion. The limied range of acion of he srong nuclear force plays an imporan role in he sabiliy of he nucleus. For a nucleus o be sable, he elecrosaic repulsion beween he proons mus be balanced by he aracion beween he nucleons due o he srong nuclear force. Bu one proon repels all oher proons wihin he nucleus, since he elecrosaic force has such a long range of acion. In conras, a proon or a neuron aracs only is neares neighbors via he srong nuclear force. s he number Z of proons in he nucleus

4 increases under hese condiions, he number of neurons has o increase even more, if sabiliy is o be mainained. Figure 31.2 shows a plo of versus Z for naurally occurring elemens ha have sable nuclei. For reference, he plo also includes he sraigh line ha represens he condiion Z. Wih few excepions, he poins represening sable greaer han he number of proons as he aomic number Z increases. s more and more proons occur in a nucleus, here comes a poin when a balance of repulsive and aracive forces canno be achieved by an increased number of neurons. Evenually, he limied range of acion of he srong nuclear force prevens exra neurons from balancing he long-range elecric repulsion of exra proons. The sable nucleus wih 209 he larges number of proons (Z 83) is ha of bismuh, 83Bi, which conains 126 neurons. ll nuclei wih more han 83 proons (e.g., uranium, Z 92) are unsable and sponaneously break apar or rearrange heir inernal srucures as ime passes. This sponaneous disinegraion or rearrangemen of inernal srucure is called radioaciviy, in 1896 by he French physicis Henri Becquerel ( ). Secion 31.4 discusses radioaciviy in greaer deail. Z Z Because of he srong nuclear force, he nucleons in a sable nucleus are held ighly ogeher. Therefore, energy is required o separae a sable nucleus ino is consiuen proons and neurons, as Figure 31.3 illusraes. The more sable he nucleus is, he greaer is he amoun of energy needed o break i apar. The required energy is called he binding energy of he nucleus. Two ideas ha we have sudied previously come ino play as we discuss he binding energy of a nucleus. These are he res energy of an objec (Secion 28.6) and mass (Secion 4.2). In Einsein s heory of special relaiviy, energy and mass are equivalen; in fac, he res energy E 0 and he mass m are relaed via E 0 mc 2 (Equaion 28.5), where c is he speed of ligh in a vacuum. Therefore, a change E 0 in he res energy of he sysem is equivalen o a change m in he mass of he sysem, according o E 0 ( m)c 2. We see, hen, ha he binding energy used in Figure 31.3 o disassemble he nucleus appears as exra mass of he separaed and saionary nucleons. In oher words, he sum of he individual masses of he separaed proons and neurons is greaer by an amoun m han he mass of he sable nucleus. The difference in mass m is known as he mass defec of he nucleus. s Example 2 shows, he binding energy of a nucleus can be deermined from he mass defec according o Equaion 31.3: Binding energy (Mass defec)c 2 ( m)c 2 (31.3) Wih few excepions, he naurally occurring sable nuclei have a number of neurons ha equals or exceeds he number Z of proons. Each do in his plo represens a sable nucleus. Energy, called he binding energy, mus be supplied o break he nucleus apar ino is consiuen proons and neurons. Each of he separaed nucleons is a res and ou of he range of he forces of he oher nucleons. Z The mos abundan isoope of helium has a 4 2He nucleus whose mass is kg. For (a) he mass defec and (b) he binding energy. The symbol 4 2He indicaes ha he helium nucleus conains Z 2 proons and neurons. To obain he mass defec m ual masses of he separaed proons and neurons. Then we subrac from his sum he mass of he 4 He nucleus. Finally, we use Equaion 31.3 o calculae he binding energy from he value for m. 2 (a) nucleons is 2( kg) 2( kg) kg Two proons This value is greaer han he mass of he inac Two neurons 4 2He m kg kg nucleus, and he mass defec is kg

5 (b) ccording o Equaion 31.3, he binding energy is Binding energy Usually, binding energies are expressed in energy unis of elecron vols insead of joules (1 ev J): Binding energy ( m)c 2 ( kg)( m/s) J ( J) 1 ev J ev 28.3 MeV In his resul, one million elecron vols is denoed by he uni MeV. The value of 28.3 MeV is more han wo million imes greaer han he energy required o remove an orbial elecron from an aom. In calculaions such as ha in Example 2, i is cusomary o use he aomic mass uni (u) insead of he kilogram. s inroduced in Secion.1, he aomic mass uni is one-welfh of he mass of a 12 6C aom of carbon. In erms of his uni, he mass of a 12 6C aom is exacly 12 u. Table 31.1 also gives he masses of he elecron, he proon, and he neuron in aomic mass unis. For fuure calculaions, he energy equivalen of one aomic mass uni can be deermined by observing ha he mass of a proon is kg or u, so ha and 1 u (1 u) E 0 ( m)c 2 ( kg)( m/s) J In elecron vols, herefore, one aomic mass uni is equivalen o 1 u ( J) kg u 1 ev J kg ev MeV Daa ables for isoopes, such as he able in ppendix F, give masses in aomic mass unis. Typically, however, he given masses are no nuclear masses. They are aomic masses ha is, he masses of neural aoms, including he mass of he orbial elecrons. Example 3 deals again wih he 4 2He nucleus and shows how o ake ino accoun he effec of he orbial elecrons when using such daa o deermine binding energies. The aomic mass of helium 4 is u, and he aomic mass of hydrogen 1 2He 1H is u. Using aomic mass unis insead of kilograms, obain he binding energy of he 4 He nucleus. To deermine he binding energy, we calculae he mass defec in aomic mass unis and hen use he fac ha one aomic mass uni is equivalen o MeV of energy. The mass of u for 4 2He includes he mass of he wo elecrons in he neural helium aom. To calculae he mass defec, we mus subrac u from he sum of he individual masses of he nucleons, including he mass of he elecrons. s Figure 31.4 illusraes, he elecron mass will be included if he masses of wo hydrogen aoms are used in he calculaion insead of he masses of wo proons. The mass of a 1 1H hydrogen aom is given in Table 31.1 as u, and he mass of a neuron as u. 2 Daa ables usually give he mass of he neural aom (including he orbial elecrons) raher han he mass of he nucleus. When daa from such ables are used o deermine he mass defec of a nucleus, he mass of he orbial elecrons mus be aken ino accoun, as his drawing illusraes 4 for he 2He isoope of helium. See Example 3.

6 plo of binding energy per nucleon versus he nucleon number. The sum of he individual masses is 2( u) 2( u) u Two hydrogen aoms Two neurons The mass defec is m u u u. Since 1 u is equivalen o MeV, he binding energy is Binding energy 28.3 MeV, which maches he resul obained in Example 2. To see how he nuclear binding energy varies from nucleus o nucleus, i is necessary o compare he binding energy for each nucleus on a per-nucleon basis. The graph in Figure 31.5 shows a plo in which he binding energy divided by he nucleon number is ploed agains he nucleon number iself. In he graph, he peak for he 2 4 He isoope of helium indicaes ha he 4 2He nucleus is paricularly sable. The binding energy per nucleon increases rapidly for nuclei wih small masses and reaches a maximum of approximaely 8.7 MeV/nucleon for a nucleon number of abou 60. For greaer nucleon numbers, he binding energy per nucleon decreases gradually. Evenually, he binding energy per nucleon decreases enough so Bi nucleus of bismuh are unsable and hence radioacive. When an unsable or radioacive nucleus disinegraes sponaneously, cerain kinds of paricles and/or high-energy phoons are released. These paricles and phoons are collecively called rays. Three kinds of rays are produced by naurally occurring

7 Conservaion Laws 1. Mass/Energy (Secions 6.8 and 28.6) 2. Elecric Charge (Secion 18.2) 3. Linear Momenum (Secion 7.2) 4. ngular Momenum (Secion 9.6) 5. ucleon umber uclear Processes 1. Radioacive Decay decay, decay, and decay The conservaion laws lised a he lef side of his char are obeyed when a nucleus undergoes radioacive decay. The hree ypes of naurally occurring decay are decay, decay, and decay. uclear medicine uses radioacive decay o produce scans of organs. This phoograph shows a nuclear scan of wo kidneys, he one on he lef displaying an invasive cancer. (ISM/Phooake) radioaciviy: rays, rays, and rays. of he Greek alphabe, alpha ( ), bea ( ), and gamma ( ), o indicae he exen of heir abiliy o penerae maer. rays are he leas peneraing, being blocked by a hin ( 0.01 mm) shee of lead, whereas rays penerae lead o a much greaer disance ( 0.1 mm). rays are he mos peneraing and can pass hrough an appreciable hickness ( 100 mm) of lead. The nuclear disinegraion process ha produces,, and rays mus obey he laws of physics ha we have sudied in previous chapers. s he Conceps-a-a-Glance char in Figure 31.6 reminds us, hese laws are called conservaion laws because each of hem deals wih a propery (such as mass/energy, elecric charge, linear momenum, and angular momenum) ha is conserved or does no change during a vaion of nucleon number. In all radioacive decay processes i has been observed ha he number of nucleons (proons plus neurons) presen before he decay is equal o he number of nucleons afer he decay. Therefore, he number of nucleons is conserved during a nuclear disinegraion. s applied o he disinegraion of a nucleus, he conservaion laws require ha he energy, elecric charge, linear momenum, angular momenum, and nucleon number ha a nucleus possesses mus remain unchanged when i disinegraes ino nuclear fragmens and accompanying,, or rays. The hree ypes of radioaciviy ha occur naurally can be observed in a relaively simple experimen. piece of radioacive maerial is placed a he boom of a narrow hole in a lead cylinder. The cylinder is locaed wihin an evacuaed chamber, as Figure 31.7 ographic plae is posiioned o he righ of he hole. Three spos appear on he developed plae, which are associaed wih he radioaciviy of he nuclei in he maerial. Since movexperimen reveals ha wo ypes of radioaciviy ( and rays, as i urns ou) consis of charged paricles, whereas he hird ype ( rays) does no. and consis of moving charged paricles. uncharged.

8 When a nucleus disinegraes and produces rays, i is said o undergo decay. Experimenal evidence shows ha rays consis of posiively charged paricles, each one being he 4 2He nucleus of helium. Thus, an paricle has a charge of 2e and a nucleon number of 4. Since he grouping of 2 proons and 2 neurons in a 2 4 He nucleus is paricularly sable, as we have seen in connecion wih Figure 31.5, i is no surprising ha an paricle can be ejeced as a uni from a more massive unsable nucleus. Figure 31.8 shows he disinegraion process for one example of decay: Paren Daugher paricle nucleus nucleus (helium (uranium) (horium) nucleus) The original nucleus is referred o as he paren nucleus (P), and he nucleus remaining afer disinegraion is called he daugher nucleus (D). Upon emission of an paricle, 238 he uranium 92U paren is convered ino he 90Th daugher, which is an isoope of horium. The paren and daugher nuclei are differen, so decay convers one elemen ino anoher, a process known as ransmuaion. Elecric charge is conserved during decay. In Figure 31.8, for insance, 90 of he 92 proons in he uranium nucleus end up in he horium nucleus, and he remaining 2 proons are carried off by he paricle. The oal number of 92, however, is he same before and afer disinegraion. decay also conserves he number of nucleons, because he number is he same before (238) and afer ( 4) disinegraion. Consisen wih he conservaion of elecric charge and nucleon number, he general form for decay is decay ZP U 90 Th 2 He 4 Z 2D 4 2He Paren Daugher paricle nucleus nucleus (helium nucleus) When a nucleus releases an paricle, he nucleus also releases energy. In fac, he energy released by radioacive decay is responsible, in par, for keeping he inerior of he earh ho and, in some places, even molen. The following example shows how he conservaion of mass/energy can be used o deermine he amoun of energy released in decay. decay occurs when an unsable paren nucleus emis an paricle and in he process is convered ino a differen, or daugher, nucleus. 238 The aomic mass of uranium 92U is u, ha of horium 90Th is.0436 u, and ha of an paricle He is u. Deermine he energy released when decay convers 92U ino Th. 90 Decay and he Release of Energy Since energy is released during he decay, he combined mass of he 90Th daugher nucleus and he paricle is less han he mass of he 92U paren nucleus. The difference 238 in mass is equivalen o he energy released. We will deermine he difference in mass in aomic mass unis and hen use he fac ha 1 u is equivalen o MeV. The decay and he masses are shown below: U 90Th u.0436 u u u 4 2He The decrease in mass, or mass defec for he decay process, is u u u. s usual, he masses are aomic masses and include he mass of he orbial elecrons. 238 Bu his causes no error here because he same oal number of elecrons is included for 92U, on he one hand, and for plus 4 90Th 2He, on he oher. Since 1 u is equivalen o MeV, he released energy is 4.3 MeV. When decay occurs as in Example 4, he energy released appears as kineic energy of he recoiling 90Th nucleus and he paricle, excep for a small porion carried away

9 as a ray. Concepual Example 5 discusses how he 90Th nucleus and he paricle share in he released energy. smoke deecor. In Example 4, he energy released by he decay of U is found o be 4.3 MeV. Since his energy is carried away as kineic energy of he recoiling 90Th nucleus and he paricle, i follows ha KE Th KE 4.3 MeV. However, KE Th and KE are no equal. Which paricle carries away more kineic energy, he Th nucleus or he paricle? Kineic energy depends on he mass m and speed of a paricle, 1 since KE m 2 2 (Equaion 6.2). The 90Th nucleus has a much greaer mass han he paricle, and since he kineic energy is proporional o he mass, i is emping o conclude ha he 90Th nucleus has he greaer kineic energy. This conclusion is no correc, however, since i does no ake ino accoun he fac ha he 90Th nucleus and he paricle have differen speeds afer he decay. In fac, we expec he horium nucleus o recoil wih he smaller speed precisely because 238 i has he greaer mass. The decaying 92U is like a faher and his young daugher on ice skaes, pushing off agains one anoher. The more massive faher recoils wih much less speed han he daugher. We can use he principle of conservaion of linear momenum o verify our expecaion. s Secion 7.2 discusses, he conservaion principle saes ha he oal linear momenum of an isolaed sysem remains consan. n isolaed sysem is one for which he vecor sum of ion. I is saionary iniially, and since momenum is mass imes velociy, is iniial momenum 90Th paricle and has a m Th Th m. ccording o momenum conservaion, he iniial and m Th Th m 0. Th m /m Th. Since m Th is much greaer han m, we can see ha he speed of he horium nucleus is less han he speed of he paricle. Moreover, he kineic energy depends on he square of he speed and he paricle has he greaer kineic energy. Problem U One widely used applicaion of decay is in smoke deecors. Figure 31.9 illusraes how a smoke deecor operaes. Two small and parallel meal plaes are separaed by a disance of abou one cenimeer. iny amoun of radioacive maerial a he cener of one of he plaes emis paricles, which collide wih air molecules. During he collisions, he air molecules are ionized o form posiive and negaive ions. The volage from a baery causes one plae o be posiive and he oher negaive, so ha each plae aracs ions of opposie charge. s a resul here is a curren in he circui aached o he plaes. The presence of smoke paricles beween he plaes reduces he curren, since he ions ha collide wih a smoke paricle are usually neuralized. The drop in curren ha smoke paricles cause is used o rigger an alarm. decay occurs when a neuron in an unsable paren nucleus decays ino a proon and an elecron, he elecron being emied as he paricle. In he process, he paren nucleus is ransformed ino he daugher nucleus. The sie o ha of he posiively charged rays. Consequenly, hese rays, which are he mos common kind, consis of negaively charged paricles or paricles. Experimen shows ha paricles are elecrons. s an illusraion of decay, consider he horium 90Th nucleus, which decays by emiing a paricle, as in Figure 31.10: Paren Daugher paricle nucleus nucleus (elecron) (horium) ( proacinium) decay, like decay, causes a ransmuaion of one elemen ino anoher. In his case, horium Th is convered ino proacinium Pa. The law of conservaion of charge is 90 90Th 91Pa e

10 obeyed, since he ne number of posiive charges is he same before (90) and afer (91 1) he emission. The law of conservaion of nucleon number is obeyed, since he nucleon number remains a. The general form for decay is decay ZP Z Paren Daugher paricle nucleus nucleus (elecron) The elecron emied in decay does no acually exis wihin he paren nucleus and is no one of he orbial elecrons. Insead, he elecron is creaed when a neuron decays ino a proon and an elecron; when his occurs, he proon number of he paren nucleus increases from Z o Z 1 and he nucleon number remains unchanged. The newly creaed elecron is usually fas-moving and escapes from he aom, leaving behind a posiively charged aom. Example 6 illusraes ha energy is released during decay, jus as i is during decay, and ha he conservaion of mass/energy applies. 1 D 0 1e The aomic mass of horium 90Th is u, and he aomic mass of proacinium is u. Find he energy released when decay changes Th ino Pa Pa much he mass has decreased because of he decay and hen calculaing he equivalen energy. The decay and he masses are shown below: 90Th u 0 91Pa 1 e u When he 90Th nucleus of a horium aom is convered ino a 91Pa nucleus, he number of orbial elecrons remains he same, so he resuling proacinium aom is missing one orbial elecron. However, he given mass includes all 91 elecrons of a neural proacinium aom. In effec, hen, he value of u for 91Pa already includes he mass of he paricle. The mass decrease ha accompanies he decay is u u u The equivalen energy (1 u MeV) is 0.27 MeV. This is he maximum kineic energy ha he emied elecron can have. ( 91 Pa), ( 10 e) second kind of decay someimes occurs.* In his process he paricle emied by he nucleus is a posiron raher han an elecron. posiron, also called a paricle, has he same mass as an elecron bu carries a charge of e insead of e. The disinegraion process for decay is decay ZP Paren Daugher paricle nucleus nucleus ( posiron) The emied posiron does no exis wihin he nucleus bu, raher, is creaed when a nuclear proon is ransformed ino a neuron. In he process, he proon number of he paren nucleus decreases from Z o Z 1, and he nucleon number remains he same. s wih decay, he laws of conservaion of charge and nucleon number are obeyed, and here is a ransmuaion of one elemen ino anoher. Z 1 D 0 1e * hird kind of decay also occurs in which a nucleus pulls in, or capures, one of he orbial elecrons from ouside he nucleus. The process is called elecron capure, or K capure, since he elecron normally comes from he innermos, or K, shell.

11 The nucleus, like he orbial elecrons, exiss only in discree energy saes or levels. When a nucleus changes from an excied energy sae (denoed by an aserisk *) o a lower energy sae, a phoon is emied. The process is similar o he one discussed in Secion 30.3 for he phoon emission ha leads o he hydrogen aom line specrum. Wih nuclear energy levels, however, he phoon has a much greaer energy and is called a ray. The decay process is wrien as follows: decay Z P* Excied Lower ray energy sae energy sae decay does no cause a ransmuaion of one elemen ino anoher. In he nex example he wavelengh of one paricular -ray phoon is deermined. Z P Wha is he wavelengh (in vacuum) of he MeV -ray phoon emied by radium Ra? The wavelengh of he phoon is relaed o he speed of ligh and he frequency of he phoon. The frequency is no given, bu i can be obained from he MeV energy of he phoon. The phoon is emied wih his energy when he nucleus changes from one energy sae o a lower energy sae. The energy is he difference E beween he wo nuclear energy levels, in a way very similar o ha discussed in Secion 30.3 for he energy levels of he elecron in he hydrogen aom. In ha secion, we saw ha he energy difference E is relaed o he frequency f and Planck s consan h, so ha we will be able o obain he frequency from he given energy value. The following able summarizes he available daa: Descripion Symbol Value Commen Energy of -ray phoon E MeV Will be convered ino joules. Unknown Variable Wavelengh of -ray phoon? E of a - h E = hf. f The Relaion of Wavelengh o Frequency The phoon wavelengh is relaed o he phoon frequency f and he speed c of ligh in a vacuum according o Equaion 16.1, as shown a he righ. We have no value for he frequency, so we urn o Sep 2 o evaluae i. c f? (16.1) Phoon Frequency and Phoon Energy Secion 30.3 discusses he fac ha he phoon emied when he elecron in a hydrogen aom changes from a higher o a lower energy level has an energy E, which is he difference beween he energy levels. similar siuaion exiss here when he nucleus changes from a higher o a lower energy level. The -ray phoon ha is emied has an energy E given by E hf (Equaion 30.4). Solving for he frequency, we obain f E h f c f E h (16.1) which we can subsiue ino Equaion 16.1, as indicaed a he righ.

12 The wavelengh of he -ray phoon is hc E ( J s)( m/s) J ( ev) 1 ev oe ha we have convered he value of E ev ino joules by using he fac ha 1 ev J. Problem 26 c f c E h m Gamma Knife radiosurgery is becoming a very promising medical procedure for reaing cerain problems of he brain, including benign and cancerous umors as well as blood vessel malformaions. The procedure, which involves no knife a all, uses powerful, highly focused beams of rays aimed a he umor or malformaion. The rays are emied by a radioacive cobal-60 source. s Figure 31.11a illusraes, he paien wears a proecive meal helme ha is perforaed wih many small holes. Par b shows ha he holes focus he rays o a single iny arge wihin he brain. The arge issue hus receives a very inense dose of radiaion and is desroyed, while he surrounding healhy issue is undamaged. Gamma Knife surgery is a noninvasive, painless, and bloodless procedure ha is ofen performed under local aneshesia. Hospial says are 70 o 90% shorer han wih convenional surgery, and paiens ofen reurn o work wihin a few days. n exercise hallium hear scan is a es ha uses radioacive hallium o produce images of he hear muscle. When combined wih an exercise es, such as walking on a readmill, he hallium scan helps idenify regions of he hear ha do no receive enough blood. The scan is especially useful in diagnosing he presence of blockages in he coronary areries, which supply oxygen-rich blood o he hear muscle. During he es, a small amoun of hallium is injeced ino a vein while he paien walks on a readmill. The hallium aaches o he red blood cells and is carried hroughou he body. The hallium eners he hear muscle by way of he coronary areries and collecs in hear-muscle cells ha 201 come ino conac wih he blood. The hallium isoope used, 81Tl, emis rays, which a special camera records. Since he hallium reaches hose regions of he hear ha have an (a) (b) (a) In Gamma Knife radiosurgery, a proecive meal helme conaining many small holes is placed over he paien s head. ( Cusom Medical Sock Phoo) (b) The holes focus he beams of rays o a iny arge wihin he brain.

13 reduced due o arerial blockages (see Figure 31.12). second se of images is aken several hours laer, while he paien is resing. These images help differeniae beween regions afer he exercise) and regions ha are permanenly damaged due o, for example, a previimporan medical echnique. In reaing cancer, for example, he mehod of delivery should ideally apply a high dose of radiaion o a malignan umor in order o kill i, while applying only a small (non-damaging) dose o healhy surrounding issue. Brachyherapy implans offer such a delivery mehod. In his ype of reamen, radioacive isoopes are formed ino small seeds and implaned direcly in he umor according o a predesigned paern. The energy and ype of radiaion emied by he isoopes can be exploied o opimize a reamen design and minimize damage o healhy issue. Seeds conaining iridium Ir are used o rea many cancers, and seeds conaining iodine I and palladium Pd are used for prosae cancer. Research has also indicaed ha brachyherapy implans may have an imporan role o play in he reamen of aherosclerosis, in which blood vessels become blocked wih plaque. Such blockages are ofen reaed using he echnique of balloon angioplasy. Wih he aid of a caheer insered ino an occluded coronary arery, a balfor he arerial wall) a he sie of he blockage. Someimes he arerial wall is damaged in his process, and as i heals, he arery ofen becomes blocked again. Brachyherapy implans (using iridium Ir or phosphorus 15P, 32 for insance) have been found o inhibi repea blockages following angioplasy. n exercise hallium hear scan indicaes regions of he hear ha The Super-Kamiokande neurino deecor in Japan consiss of a seel cylindrical ank conaining 12.5 million gallons of ulrapure waer. Is inner wall is lined wih phoomuliplier ubes. ( Kyodo ews Inernaional) When a paricle is emied by a radioacive nucleus, energy is simulaneously released, as Example 6 illusraes. Experimenally, however, i is found ha mos paricles do no have enough kineic energy o accoun for all he energy released. If a paricle carries away only par of he energy, where does he remainder go? The quesion puzzled physiciss unil 1930, when Wolfgang Pauli proposed ha par of he energy is carried away by anoher paricle ha is emied along wih he paricle. This addiional paricle is called he neurino, ) is used o symbolize he neurino. For insance, he decay of horium 90Th (see Secion 31.4) is more correcly wrien as 90Th 91Pa 1 0 e The bar above he is included because he neurino emied in his paricular decay process is an animaer neurino, or anineurino. normal neurino ( wihou he bar) is emied when decay occurs.

14 ineracs very weakly wih maer. For example, he average neurino can penerae one ligh-year of lead (abou m) wihou ineracing wih i. Thus, even hough rillions of neurinos pass hrough our bodies every second, hey have no effec. lhough difdeecor in Japan. I is locaed 915 m underground and consiss of a seel cylindrical ank, en sories all, whose inner wall is lined wih phoomuliplier ubes (see Secion wih he waer molecules produce ligh paerns ha he phoomuliplier ubes deec. quesion is imporan because neurinos are so pleniful in he universe. Even a very small could have an effec on he formaion of galaxies. In 1998 he Super-Kamiokande deecmass. (The mass of he elecron neurino is less han % of he mass of an elecron.) mass were zero, like ha of a phoon, i would ravel a he speed of ligh. The emission of neurinos and paricles involves a force called he weak nuclear force because i is much weaker han he srong nuclear force. I is now known ha he weak nuclear force and he elecromagneic force are wo differen manifesaions of a single, more fundamenal force, he elecroweak force. The heory for he elecroweak force was developed by Sheldon Glashow (1932 ), bdus Salam ( ), and Seven Weinberg (1933 ), who shared a obel Prize for heir achievemen in The elecroweak force, he graviaional force, and he srong nuclear force are he hree fundamenal forces in naure. The quesion of which radioacive nucleus in a group of nuclei disinegraes a a given insan is decided like he winning numbers in a sae loery: individual disinegraions occur randomly. s ime passes, he number of paren nuclei decreases, as Figure 31. shows. This graph of versus ime indicaes ha he decrease occurs in a smooh fashion, wih approaching zero afer enough ime has passed. To help half-life T 1/2 of a radioacive isoope as he ime required for one-half of he nuclei presen o disinegrae. For example, radium Ra has a half-life of 1600 years, because i akes his amoun of ime for one-half of a given quaniy of his isoope o disinegrae. In anoher 1600 years, one-half of he remaining radium aoms will have disinegraed, leaving only one-fourh of he original number inac. In Figure 31., he number of nuclei presen a ime 0 s is 0, and he 1 number presen a T 1/2 is 2 0. The number presen a 2T 1/2 is 4 0, and so on. The value of he half-life depends on he naure of he radioacive nucleus. Values ranging from a fracion of a second o billions of years have been found (see Table 31.2). Radon Rn is a naurally occur- 226 ring radioacive gas produced when radium 88Ra undergoes decay. There is a naionwide concern abou radon as a healh hazard because radon in he soil is gaseous and can ener he basemen of homes hrough cracks in he foundaion. (I should be noed, however, ha he mechanism of indoor radon enry is no well undersood and ha enry via foundaion cracks is likely only par of he sory.) Once inside, he concenraion of radon can rise markedly, depending on he ype of housing consrucion and he concenraion of radon in he surrounding soil. Radon gas decays ino daugher nuclei ha are also radioacive. The radioacive nuclei can aach o dus and smoke paricles ha can be inhaled, and hey remain in he lungs o release issue-damaging radiaion. Prolonged exposure o high levels of radon can lead o lung cancer. Since radon gas concenraions can be measured wih inexpensive monioring devices, i is recommended ha all homes be esed for radon. Example 8 deals wih he half-life of radon Rn. 1 Isoope T T T The half-life T 1/2 of a radioacive decay is he ime in which one-half of he radioacive nuclei disinegrae. T Half-Life Polonium 2 84 Po s Krypon 89 36Kr 3.16 min Radon Rn 3.83 d Sronium 90 38Sr 29.1 yr Radium Ra yr Carbon 6 C yr Uranium U yr Indium In yr

15 Suppose ha radon aoms are rapped in a basemen a he ime he basemen is sealed agains furher enry of he gas. The half-life of radon is 3.83 days. How many radon aoms remain afer 31 days? During each half-life, he number of radon aoms is reduced by a facor of wo. Thus, we deermine he number of half-lives here are in a period of 31 days. he end of each half-life we reduce he number of radon aoms presen a he beginning of ha half-life by a facor of wo. In a period of 31 days here are (31 days)/(3.83 days) 8.1 half-lives. In 8 halflives he number of radon aoms is reduced by a facor of Ignoring he difference ( )/ The aciviy of a radioacive sample is he number of disinegraions per second ha occur. Each ime a disinegraion occurs, he number of radioacive nuclei decreases. s a resul, he aciviy can be obained by dividing, he change in he number of nuclei, by, he ime inerval during which he change akes place; he average aciviy over he ime inerval is he magniude of /, or /. Since he decay of any individual nucleus is compleely random, he number of disinegraions per second ha occurs in a sample is proporional o he number of radioacive nuclei presen, so ha (31.4) where is a proporionaliy consan referred o as he decay consan. The minus sign is presen in his equaion because each disinegraion decreases he number of nuclei originally presen. The SI uni for aciviy is he becquerel (Bq), named afer noine Becquerel ( ). One becquerel equals one disinegraion per second. civiy is also measured in erms of a uni called he curie (Ci), in honor of Marie ( ) and Pierre ( ) Curie, he discoverers of radium and polonium. Hisorically, he curie was chosen as a uni because i is roughly he aciviy of one gram of pure radium. In erms of becquerels, 1 Ci Bq The aciviy of he radium pu ino he dial of a wach o make i glow in he dark is abou Bq, and he aciviy used in radiaion herapy for cancer is approximaely a billion imes greaer, or Bq. The mahemaical expression for he graph of versus shown in Figure 31. can be obained from Equaion 31.4 wih he aid of calculus. The resul for he number of radioacive nuclei presen a ime is 0 e (31.5) assuming ha he number presen a 0 s is 0. The exponenial e has he value e , and many calculaors provide he value of e x. We can relae he half-life T 1/2 of a radioacive nucleus o is decay consan in he following manner. By subsiuing 0 and 1 1 T 2 e 1/2. 2 T1/2 logarihm of boh sides of his equaion reveals ha ln 2 or T 1/2 ln T 1/2 The following example illusraes he use of Equaions 31.5 and (31.6) s in Example 8, suppose ha here are radon aoms (T 1/ days or s) rapped in a basemen. (a) How many radon aoms remain afer 31 days? Find he aciviy (b) jus afer he basemen is sealed agains furher enry of radon and (c) 31 days laer.

16 The number of radon aoms remaining afer a ime is given by 0 e, where is he original number of aoms when 0 s and is he decay consan. The decay consan is relaed o he half-life T 1/2 of he radon aoms by 0.693/ T 1/2. The aciviy can be obained from Equaion 31.4, /. (a) The decay consan is and he number of radon aoms remaining afer 31 days is (31.6) (31.5) This value is slighly less han ha found in Example 8 because here we ignored he difference beween 8.0 and 8.1 half-lives. (b) The aciviy can be obained from Equaion 31.4, provided he decay consan is expressed in reciprocal seconds: Thus, he number of disinegraions per second is T 1/ days 0 e ( )e (0.181 days 1 )(31 days) T 1/ s days s 1 ( s 1 )( ) 63 disinegraions/s The aciviy is he magniude of /, so iniially civiy 63 Bq. (31.6) (31.4) (c) From par (a), he number of radioacive nuclei remaining a he end of 31 days is , and reasoning similar o ha in par (b) reveals ha civiy 0.23 Bq. One imporan applicaion of radioaciviy is he deerminaion of he age of archaeological or geological samples. If an objec conains radioacive nuclei when i is formed, hen he decay of hese nuclei marks he passage of ime like a clock, half of he nuclei disinegraing during each half-life. If he half-life is known, a measuremen of he number of nuclei presen oday relaive o he number presen iniially can give he age of he sample. ccording o Equaion 31.4, he aciviy of a sample is proporional o he number of radioacive nuclei, so one way o obain he age is o compare presen aciviy wih iniial aciviy. more accurae way is o deermine he presen number of radioacive nuclei wih he aid of a mass specromeer. The presen aciviy of a sample can be measured, bu how is i possible o know wha he original aciviy was, perhaps housands of years ago? Radioacive daing mehods enail cerain assumpions ha make i possible o esimae he original aciviy. For insance, he in a cave in Mexico in They are hough o be abou 2300 years old. Radioacive daing is one of he echniques used o deermine he age of such remains. ( David guilar/ Reuers/Landov LLC)

17 radiocarbon echnique uilizes he 6C isoope of carbon, which undergoes decay wih a half-life of 5730 yr. This isoope is presen in he earh s amosphere a an equilibrium concenraion of abou one aom for every aoms of normal carbon 6C. I is ofen assumed* ha his value has remained consan over he years because 6C is creaed when cosmic rays inerac wih he earh s upper amosphere, a producion mehod ha offses he loss via decay. Moreover, nearly all living organisms inges he equilibrium concen- raion of 6C. However, once an organism dies, meabolism no longer susains he inpu of 6C, and decay causes half of he 6C nuclei o disinegrae every 5730 years. Example 10 illusraes how o deermine he 6C aciviy of one gram of carbon in a living organism. 12 (a) Deermine he number of carbon 6C aoms presen for every gram of carbon 6C in a living organism. Find (b) he decay consan and (c) he aciviy of his sample. The oal number of carbon 12 6C aoms in one gram of carbon 12 6C is equal o he corresponding number of moles imes vogadro s number (see Secion.1). Since here is only one 6C aom for every aoms of 12 6C, he number of 6C aoms is equal o he 12 oal number of aoms divided by C. The decay consan for 6C is 0.693/T 1/2, where T 1/2 is he half-life. The aciviy is equal o he magniude of /, which is equal o he decay consan imes he number of C aoms presen, according o Equaion (a) One gram of carbon 6C (aomic mass 12 u) is equivalen o 1.0/12 mol. Since vogadro s number is aoms/mol and since here is one aom for every C 12 aoms of C, he number of C aoms is 6 6 umber of 6C aoms for every 1.0 gram of carbon 12 6C mol aoms mol (b) Since he half-life of C is 5730 yr ( s), he decay consan is aoms T 1/ s s 1 (31.6) (c) Equaion 31.4 indicaes ha /, so he magniude of / is. civiy of 6C for every 1.0 gram of 12 carbon 6 C in a living organism ( s 1 )( aoms) 0.23 Bq n organism ha lived housands of years ago presumably had an aciviy of abou 0.23 Bq per gram of carbon. When he organism died, he aciviy began decreasing. From a sample of he remains, he curren aciviy per gram of carbon can be measured and compared o he value of 0.23 Bq o deermine he ime ha has ranspired since deah. This procedure is illusraed in Example 11. *The assumpion ha he 6 C concenraion has always been a is presen equilibrium value has been evaluaed by comparing 6 C ages wih ages deermined by couning ree rings. More recenly, ages deermined using he 238 radioacive decay of uranium 92U have been used for comparison. These comparisons indicae ha he equilib- rium value of he 6 C concenraion has indeed remained consan for he pas 1000 years. However, from here back abou years, i appears ha he 6 C concenraion in he amosphere was larger han is presen

18 On Sepember 19, 1991, German ouriss on a walking rip in he Ialian lps found a Sone-ge raveler, laer dubbed he Ice Man, whose body had become rapped in a glacier. Figure shows he well-preserved remains, which were daed using he radiocarbon mehod. Maerial found wih he body had a 6C aciviy of abou Bq per gram of carbon. Find he age of he Ice Man s remains. In he radiocarbon mehod, he number of radioacive nuclei remaining a a given insan is relaed o he number presen iniially, he ime ha has passed since he Ice Man died, and he decay consan for 6C. Thus, o deermine he age of he remains, we will need informaion abou he number of nuclei presen when he body was discovered and he number presen iniially, which can be relaed o he aciviy of he maerial found wih he body and he iniial aciviy. To deermine he age, we will also need he decay consan, which can be obained from he half-life of 6C. We have he following daa: Descripion Symbol Value Commen Explici Daa civiy of maerial found wih body Bq This is he aciviy per gram of carbon. Implici Daa Half-life of 6C T 1/2 Iniial aciviy of maerial found wih body Bq This aciviy is assumed for one gram of carbon in a living organism. Unknown Variable ge of Ice Man s remains? The wo scieniss in his phoograph are sudying he Ice Man or Oezi, as he is also called. His frozen remains and various arifacs were discovered in he ice of a glacier in he Ialian lps in Radiocarbon daing has revealed his age. ( FP/Gey Images ews) Radioacive Decay The number of radioacive nuclei presen a a ime is 0 e where 0 is he number presen iniially a 0 s and is he decay consan for 6C. Rearranging erms gives 0 e (31.5) ln 0 Solving for shows ha he age of he Ice Man s remains is given by Equaion 1 a he righ. To use his resul, we need informaion abou he raio / 0 and. We deal wih / 0 in Sep 2 and wih in Sep 3. 1? ln 0? (1) where civiy The aciviy is he number of disinegraions per second, or, is he number of disinegraions ha occur in he ime inerval. oing ha Coninued

19 Using his expression, we have ha 1 ln 0 (1) The subsiuion of his resul ino Equaion 1 is shown a he righ. We urn now o Sep 3, in order o evaluae he decay consan.? 0 0 Decay Consan The decay consan is relaed o he half-life T 1/2 according o T 1/2 which we subsiue ino Equaion 1, as shown a he righ. (31.6) T 1/2 1 ln (1) This resul reveals ha he age of he Ice Man s remains is 1 ln T 1/ oe ha his soluion implies for he aciviy ha 0 ln 0 1 This can be seen by combining he resul from Sep 2 (/ 0 / 0 ) wih Equaion 31.5 ( 0 e ). Problems 46, 58 ln 5730 yr e /T 1/2 ln Bq 0.23 Bq ln yr Radiocarbon daing is no he only radioacive daing mehod. For example, oher mehods uilize uranium U, poassium K, and lead Pb. For such mehods o be useful, he half-life of he radioacive species mus be neiher oo shor nor oo long relaive o he age of he sample o be daed, as Concepual Example 12 discusses. bole of red wine is hough o have been sealed abou 5 years ago. The wine conains a number of differen aoms, including carbon, oxygen, and hydrogen. Each of hese has a radioacive isoope. The radioacive isoope of carbon is he familiar 6C, wih a half-life of 5730 yr. 15 The radioacive isoope of oxygen is 8 O and has a half-life of s. The radioacive isoope 3 of hydrogen, called riium, is 1H; is half-life is yr. The aciviy of each of hese isoopes is known a he ime he bole was sealed. However, only one of he isoopes is useful for deermining he age of he wine accuraely from a measuremen of is curren aciviy. Which is i? 15 3 (a) 6C (b) 8 O (c) 1H aciviy o he iniial aciviy 0 (see Example 11). If he age of he sample is very small relaive o he half-life of he nuclei, relaively few of he nuclei have decayed during he wine s life, and he measured aciviy changes lile from is iniial value ( 0 ). To obain an accurae age from such a small change would require prohibiively precise measuremens. On he oher hand, if he age of he sample is many imes greaer han he half-life of he nuclei, virually all of he nuclei would have decayed, and he curren aciviy would be so small ( 0) ha i would be virually impossible o deec. The expeced age of he wine is abou 5 years. This period is only a iny fracion of he 5730-yr half-life of C. s a resul, relaively few of he C nuclei would 6 6

20 decay during he wine s life, and he curren aciviy would be nearly he same as he iniial aciviy ( 0 ), hus requiring prohibiively precise measuremens. 15 The 8 O isoope is no very useful eiher, because of is relaively shor half-life of s. During a 5-year period, so many half-lives of s would occur ha he curren aciviy would be vanishingly small ( 0) and undeecable. 3 The only remaining opion is he 1H isoope. The expeced age of 5 yr is long enough relaive o he half-life of yr ha a measurable change in aciviy will occur, bu no so long ha he curren aciviy will have compleely vanished for all pracical purposes. Problem 49 In he radioacive daing echnique ha uses he carbon 6C isoope, he relaively few 6C aoms can be deeced by measuring heir aciviy, as we have seen. I is also possible o use an acceleraor mass specromeer, such as he one in his phoograph, o deec hese aoms more accuraely. ( James King Holmes/SPL/Phoo Researchers, Inc.) When an unsable paren nucleus decays, he resuling daugher nucleus is someimes also unsable. If so, he daugher hen decays and produces is own daugher, and so on, unil a compleely sable nucleus is produced. This sequenial decay of one nucleus afer anoher is called a radioacive decay series. 238 wih uranium U: 92 Uranium 238 U 92 Thorium Th He Furhermore, Examples 8 and 9 deal wih radon Rn, which is formed down he line in he U radioacive decay series. Figure shows he enire series. several poins, branches occur because more han one kind of decay is possible for an inermediae species. Ulimaely, however, he series 206 ends wih lead 82Pb, which is sable. The U series and oher such series are he only sources of some of he radioacive elemens found in naure. Radium Ra, for insance, has a half-life of 1600 yr, which is shor 226 enough ha all he 88Ra creaed when he earh was formed billions of years ago has now disappeared. The U series 226 provides a coninuing supply of Ra, however Pa Proacinium 0 1e The radioacive decay 238 series ha begins wih uranium 92U 206 and ends wih lead 82 Pb. Half-lives are given in seconds (s), minues (m), hours (h), days (d), or years (y). The of decay ha each nucleus undergoes.

21 There are a number of devices ha can be used o deec he paricles and phoons ( rays) emied when a radioacive nucleus decays. Such devices deec he ionizaion ha hese paricles and phoons cause as hey pass hrough maer. The mos familiar deecor is he Geiger couner, which Figure illusraes. The,, or rays ener he cylinder hrough a hin window a one end. rays can also penerae direcly hrough he meal. wire elecrode runs along he cener of he ube and is kep a a high posiive volage ( V) relaive o he ouer cylinder. When a high-energy paricle or phoon eners he cylinder, i collides wih and ionizes a gas molecule. The elecron produced from he gas molecule acceleraes oward he posiive wire, ionizing oher molecules in is pah. ddiional elecrons are formed, and an avalanche of elecrons rushes oward he wire, leading o a pulse of curren hrough he resisor R. This pulse can be couned or made o produce a click in a loudspeaker. The number of couns or clicks is relaed o he number of disinegraions ha produced he paricles or phoons. The scinillaion couner is anoher imporan radiaion deecor. s Figure indicaes, his device consiss of a scinillaor mouned on a phoomuliplier ube. Ofen he scinillaor is a crysal (e.g., cesium iodide) conaining a small amoun of impuriy (hallium), bu plasic, liquid, and gaseous scinillaors are also used. In response o ionizing he phoocahode of he phoomuliplier ube. The phoocahode is made of a maerial ha emis elecrons because of he phooelecric effec. These phooelecrons are hen araced o a special elecrode kep a a volage of abou 100 V relaive o he phoocahode. The elecrode is coaed wih a subsance ha emis several addiional elecrons for every elecron sriking i. The addiional elecrons are araced o a second similar elecrode (volage 200 V), where hey generae even more elecrons. Commercial phoomuliplier ubes conain as many as 15 of hese special elecrodes, so phooelecrons resuling from a Geiger ube, he curren pulses can be couned. Ionizing radiaion can also be deeced wih several ypes of semiconducor deecors. Such devices uilize n- and p-ype maerials (see Secion 23.5), and heir operaion depends e R Geiger couner. scinillaion couner.

22 on he elecrons and holes formed in he maerials as a resul of he radiaion. One of he main advanages of semiconducor deecors is heir abiliy o discriminae beween wo paricles wih only slighly differen energies. number of insrumens provide a picorial represenaion of he pah ha highenergy paricles follow afer hey are emied from unsable nuclei. In a cloud chamber, a gas is cooled jus o he poin a which i will condense ino droples, provided nucleaing agens are available on which he droples can form. When a high-energy paricle, such as an paricle or a paricle, passes hrough he gas, he ions i leaves behind serve as nucleaing agens, and droples form along he pah of he paricle. bubble chamber works in a similar fashion, excep ha i conains a liquid ha is jus a he poin of boiling. Tiny bubbles form along he rail of a high-energy paricle passing hrough he liquid. Pahs revealed in a cloud or bubble chamber can be phoographed o provide a permanen record of he even. Figure shows a phoograph of racks in a bubble chamber. phoographic emulsion also can be used direcly o produce a record of he pah aken by a paricle of ionizing radiaion. Ions formed as he paricle passes hrough he emulsion cause silver o be deposied along he rack when he emulsion is developed. phoograph showing paricle racks in a bubble chamber. ( CER/Phoo Researchers, Inc.) of hese laws, as he Conceps-a-a-Glance char in Figure 31.6 illusraes. Two of hem are paricularly imporan in undersanding he ypes of radioaciviy ha occur and he nuclear changes ha accompany hem. These are he conservaion of elecric charge and he conservaion of nucleon number. Example 13 emphasizes heir imporance and reviews how hey are applied. 228 Thorium 90Th produces a daugher nucleus ha is radioacive. The daugher, in urn, produces 212 is own radioacive daugher, and so on. This process coninues unil bismuh 83Bi is reached. Wha are he oal number of paricles and he oal number of paricles ha are generaed in his series of radioacive decays? How many of he 90 proons in he horium nucleus are carried off by he paricles? nswer Each paricle is a helium 4 2He nucleus and carries off wo proons. Therefore, he oal number of proons carried off by he paricles is (2). How many proons are lef behind when he paricles are emied? nswer Each paricle is an elecron 0 1e and is emied when a neuron in he nucleus decays ino a proon and an elecron. Therefore, he oal number of proons lef behind by he paricles is. How many of he 228 nucleons in he horium nucleus are carried off by he paricles? nswer Each paricle is a helium 4 2He nucleus and carries off four nucleons. Therefore, he oal number of nucleons carried off by he paricles is (4). Does he deparure of a paricle aler he number of nucleons? nswer o. Each paricle is an elecron 0 1e and is emied when a neuron in he nucleus decays ino a proon and an elecron. In effec, a neuron is replaced by a proon. Bu since each is a nucleon, he number of nucleons is no changed. The overall decay process can be wrien as Th 83Bi ( 24 He) ( 10 e) Since elecric charge mus be conserved, we know ha he charge on he lef side of his reacion mus be equal o he oal charge on he righ side, he resul being (2) ( 1)