Ikhemistri yenyukliya: amandla okubopha, izindlela zokubola nama-half-life

Isilinganiso se-neutron ne-proton nebhande lokuzinza

I-nucleus iqukethe ama-proton nama-neutron, ndawonye abizwa ngokuthi ama-nucleon. Ama-proton ayaxoshana ngogesi, futhi amandla aqinile enyukliya, asebenza emabangeni amafushane kakhulu kuphela, abamba wonke ama-nucleon ndawonye. Ukuthi i-nucleus izinzile yini kuncike ikakhulukazi ekulinganeni phakathi kwama-proton nama-neutron.

Uma ubonisa ama-neutron ngokuqhathaniswa nama-proton kuma-nuclide azinzile, awela ebhandeni elincane lokuzinza. Ama-nucleus alula azinzile anamanani acishe alingane kokubili: i-nitrogen-14 inayisikhombisa kokubili. Ama-nucleus asindayo adinga ama-neutron engeziwe ukuze alinganise ukuxoshana kwama-proton okukhulayo. I-OpenStax inikeza isilinganiso se-n:p esingu-1.15 se-iron-56 no-1.52 se-lead-207. Yonke i-isotope yaso sonke isakhi esingaphezu kwe-bismuth (Z = 83) iyi-radioactive.

I-nuclide engaphandle kwebhande ibola ngendlela eyisondeza ebhandeni. Lowo mqondo owodwa ubikezela izindlela eziningi zokubola, njengoba uhlu lwezindlela zokubola olungezansi lukhombisa.

I-mass defect namandla okubopha enyukliya

I-nucleus inesisindo esincane kunama-proton nama-neutron ahlukene eyakhiwe ngawo. Isisindo esilahlekile, i-mass defect, sihambisana namandla okubopha enyukliya ngo-E = mc². Ngamayunithi esisindo se-athomu, u-1 u ulingana no-931.494 MeV (inani le-CODATA elivela ku-NIST).

Isibonelo esisebenzile 1. Thola amandla okubopha e-helium-4. Ukusebenzisa izisindo ze-athomu kugcina ama-electron elinganisiwe: ama-athomu amabili e-hydrogen-1 ahlinzeka ngama-proton amabili nama-electron amabili. I-NIST ibhala u-1.007 825 032 u we-¹H no-4.002 603 254 u we-⁴He, kanti i-CODATA inikeza u-1.008 664 916 u we-neutron. Izinhlayiya ezihlukene: 2(1.007 825 032) + 2(1.008 664 916) = 4.032 979 896 u. I-mass defect: 4.032 979 896 − 4.002 603 254 = 0.030 376 642 u. Amandla okubopha: 0.030 376 642 u × 931.494 MeV/u = 28.30 MeV, noma 7.074 MeV nge-nucleon ngayinye. I-OpenStax icaphuna u-28.4 MeV ngoba isebenzisa izisindo eziyiswe ezindaweni ezine zedesimali, okukhombisa ukuthi umehluko omncane phakathi kwezinombolo ezinkulu uzwela kangakanani ekuyiseni.

Uma kulinganiswe nge-mole, u-28.30 MeV nge-nucleus ngayinye ungu-2.73 × 10¹² J/mol. Ukushisa i-mole ye-methane kukhulula cishe u-890 kJ (kusuka kuma-enthalpy okwakheka kaSithasiselo G), ngakho ukwakha i-helium-4 kuma-nucleon ayo kukhulula amandla acishe aphindwe izigidi ezintathu nge-mole ngayinye. Amandla okubopha nge-nucleon ngayinye makhulu kakhulu eduze nenombolo yesisindo engu-56; i-OpenStax ibala u-8.820 MeV nge-nucleon ngayinye we-iron-56. Yingakho kokubili ukuhlanganisa ama-nucleus alula nokuhlukanisa asinda kakhulu kukhulula amandla.

Izindlela ezinhlanu zokubola nalokho ngayinye ekushintshayo

Indlela ngayinye yokubola ishintsha inombolo yesisindo u-A nenombolo ye-athomu u-Z ngendlela engaguquki. Ukwazi ukuthi i-nuclide ihlala ngakuluphi uhlangothi lwebhande kukutshela ukuthi yiziphi izindlela okungenzeka zenzeke.

• Ukubola kwe-alpha kukhipha i-nucleus ye-helium-4, ⁴₂He. U-A wehla ngo-4 no-Z ngo-2. Kuvamile kuma-nucleus asindayo angaphezu kwe-bismuth.
• Ukubola kwe-beta kukhipha i-electron, ⁰₋₁e, njengoba i-neutron iba yi-proton. U-A akashintshi futhi u-Z ukhuphuka ngo-1. Kwenzeka kuma-nuclide anama-neutron amaningi angaphezu kwebhande.
• Ukukhishwa kwe-positron kukhipha i-positron, ⁰₊₁e, njengoba i-proton iba yi-neutron. U-A akashintshi futhi u-Z wehla ngo-1. Kwenzeka kuma-nuclide anama-proton amaningi angaphansi kwebhande.
• Ukubanjwa kwe-electron kudonsela i-electron yangaphakathi ku-nucleus, lapho ihlangana ne-proton ukwenza i-neutron. U-A akashintshi futhi u-Z wehla ngo-1, ushintsho olufanayo nokukhishwa kwe-positron.
• Ukukhishwa kwe-gamma kukhulula i-photon enamandla aphezulu, ⁰₀γ, ivela ku-nucleus esesimweni esijabulisiwe. U-A no-Z abashintshi. Kuvame ukuhambisana nezinye izindlela.

Ukulinganisa isibalo senyukliya ngokugcina u-A no-Z

Isibalo senyukliya silinganisiwe lapho izinombolo zesisindo (ama-superscript) zihlangana zibe yisamba esifanayo nhlangothi zombili futhi nezinombolo ze-athomu (ama-subscript) zenze njalo. Inombolo ye-athomu yomkhiqizo bese ihlonza isakhi.

I-uranium-238 iba nokubola kwe-alpha: ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He. Hlola: 238 = 234 + 4 no-92 = 90 + 2. I-carbon-14 iba nokubola kwe-beta: ¹⁴₆C → ¹⁴₇N + ⁰₋₁e, lapho 6 = 7 + (−1). I-fluorine-18, esetshenziswa ezihlolweni ze-PET, iba nokukhishwa kwe-positron: ¹⁸₉F → ¹⁸₈O + ⁰₊₁e. I-potassium-40 ingaba nokubanjwa kwe-electron, i-electron ibhalwe njengesisabelo: ⁴⁰₁₉K + ⁰₋₁e → ⁴⁰₁₈Ar.

Ukuthola inhlayiya engaziwa, susa. I-thorium-234 ibola ibe yi-protactinium-234: ²³⁴₉₀Th → ²³⁴₉₁Pa + X. Ku-X, A = 234 − 234 = 0 no-Z = 90 − 91 = −1, ngakho u-X ungu-⁰₋₁e futhi lokhu kungukubola kwe-beta. Ukubikezela kuhambisana nebhande: i-carbon-14 inesilinganiso se-n:p esingu-1.33, esiphezulu ku-nucleus elula kangaka, futhi ukubola kwe-beta kusiletha ku-1.00 ku-nitrogen-14.

Izibalo ze-half-life zokubola kwe-oda lokuqala

Ukubola kwe-radioactive kuyinqubo ye-oda lokuqala: esikhathini esithile, ingxenye efanayo yama-nucleus asele iyabola, noma ngabe inani lokuqala lingakanani. I-half-life, t½, yisikhathi sokuthi ingxenye yama-nucleus ibole. Cishe ayincikile ezingeni lokushisa, engcindezini nasefomini lamakhemikhali, yilokho okwenza ibe wusizo ekulinganiseni iminyaka. Inani elisele ngemva kwesikhathi t lingu-N = N₀ × (½)^(t/t½). Ngokulinganayo, ln(N/N₀) = −kt nge-decay constant k = 0.693/t½.

Isibonelo esisebenzile 2. I-iodine-131, esetshenziselwa ukwelapha isifo se-thyroid, ino-t½ = 8.02 izinsuku (Itafula 21.2 le-OpenStax). Kusala okungakanani kwesampula engu-50.0 mg ngemva kwezinsuku ezingu-30.0? t/t½ = 30.0 ÷ 8.02 = 3.741 ama-half-life. N = 50.0 mg × (½)^3.741 = 3.74 mg. Ukulinganisela okusheshayo kuyakuqinisekisa: ngemva kwama-half-life angu-3 bekuzosala u-6.25 mg futhi ngemva kwama-half-life angu-4 u-3.13 mg, ngakho impendulo kufanele ibe phakathi kwawo.

Isibonelo esisebenzile 3. I-fluorine-18 ino-t½ = 110. amaminithi. Kuthatha isikhathi esingakanani ukuthi i-activity yayo yehle ibe ngamaphesenti angu-10.0 enani lokuqala? I-activity ihambisana nenani lama-nucleus, ngakho xazulula (½)^(t/110.) = 0.100. t = 110. min × ln(10.0) ÷ ln 2 = 365 min, cishe amahora angu-6.1. Lelo windi elifushane yilona elenza i-fluorine-18 kufanele yenziwe eduze nalapho isetshenziswa khona.

Isibonelo esisebenzile: ukulinganisa iminyaka yento yokhuni nge-radiocarbon

Izinto eziphilayo zigcina isilinganiso esingaguquki se-carbon-14 ne-carbon-12 ngokushintshana nge-carbon nendawo ezungezile. Ngemva kokufa, i-carbon-14 ibola ngo-t½ = 5730 iminyaka (isigaba 21.3 se-OpenStax) futhi ayithathelwa indawo, ngakho isilinganiso sehla ngendlela engabikezelwa.

Ithuluzi lokhuni liqukethe amaphesenti angu-28.0 e-carbon-14 etholakala okhunini oluphilayo. Xazulula 0.280 = (½)^(t/5730 y). Ukuthatha ama-logarithm kunikeza t = 5730 y × ln(1/0.280) ÷ ln 2 = 1.05 × 10⁴ iminyaka, noma cishe ama-half-life angu-1.84. Hlola ukulinganisela: ngemva kwe-half-life eyodwa kusala amaphesenti angu-50 futhi ngemva kwamabili angu-25, futhi amaphesenti angu-28.0 angaphansi nje kwamabili.

I-OpenStax ithi indlela inembile kuze kufike eminyakeni ecishe ibe ngu-30 000 futhi inikeza iminyaka enengqondo kuze kufike eminyakeni ecishe ibe ngu-50 000. Ngale kwalokho, i-carbon-14 esele incane kakhulu ukuthi ilinganiswe ngokuthembekile. Iminyaka yangempela ye-radiocarbon iphinde ilungiswe ngenxa yezinguquko zangaphambili ze-carbon-14 esemkhathini.

Amaphutha ezibalweni zenyukliya nasekubaleni ukubola

Ukuhlola okubili kubamba izinkinga eziningi: linganisa u-A no-Z ngokwehlukana kuso sonke isibalo, futhi ulinganisele ukuthi mangaki ama-half-life asedlule ngaphambi kokusebenzisa ikhalkhuleyitha.

• Ukushintshanisa ushintsho lwe-beta nolwe-positron. I-beta ikhuphula u-Z ngo-1; ukukhishwa kwe-positron nokubanjwa kwe-electron kumehlisa ngo-1.
• Ukulinganisa izinombolo zesisindo kodwa hhayi izinombolo ze-athomu, noma okuphambene.
• Ukususa izisindo zama-proton angenalutho esisindweni se-athomu ngaphandle kokubhekela ama-electron. Ukusebenzisa izisindo ze-athomu ze-hydrogen-1 kuyayigwema le nkinga.
• Ukuhlukanisa inani lokuqala ngenani lama-half-life esikhundleni sokulihlukanisa kabili ngokuphindaphindiwe.
• Ukuxuba amayunithi esikhathi, njenge-half-life ngezinsuku nesikhathi esidlulile ngamahora.
• Ukuyisa izisindo ngaphambi kokuthatha umehluko ekubaleni i-mass defect.