Su'aalo Tusaale ah oo Ka Hadlaya Burburka Beta (β)
Qulqulka shucaaca waa habka uu nucleus-ka atomiga aan degganayn u sii daayo walxaha si loo gaaro xaalad deggan. Maqaalkan, waxaan diiradda saari doonnaa qulqulka beta (β), kaas oo ah nooc ka mid ah qudhunka shucaaca. Hadafkayaga ugu weyn waa inaan fahamno qudhunka beta iyada oo loo marayo tusaalooyin iyo xalalkooda. Aan ku bilowno barashada aasaaska qudhunka beta ka hor inta aan u quusin tusaalooyinka.
Aasaaska Burburka Beta
Lumitaanka Beta wuxuu ku lug leeyahay isbeddelka qaar ka mid ah nuclei-ga atomiga iyadoo soo saaraysa walxaha beta. Waxaa jira laba nooc oo lumitaanka beta ah:
1. Lumis Beta-minus (β-): Lumiskan, neutron-ka ku jira xudunta ayaa isu beddela proton, elektaroon (oo loo yaqaan walxaha beta), iyo elektaroon antineutrino. Isle'egta falgalka waa:
\[
n \rightarrow p + e^- + \bar{\nu}_e
\]
Halkan, \(n \) waa neutron, \(p \) waa proton, \(e^- \) waa elektaroonik (beta), iyo \( \bar{\nu}_e \) waa elektaroonik antineutrino ah.
2. Beta-plus (β+) suuska: Tani waxay dhacdaa marka proton-ka ku jira xudunta uu isu beddelo neutron, positron (antielektron), iyo electron neutrino. Isla'egtu waa:
\[
p \rightarrow n + e^+ + \nu_e
\]
Halka \( e^+ \) uu yahay positron iyo \( \nu_e \) uu yahay elektaroonik neutrino.
Tusaale 1: Halaag laga jaray Beta-ka
Su'aal:
Nukliyeer kaarboon-14 ah (\( ^{14}_{6}\text{C} \)) ayaa gala burburka beta-ka yar. Go'aami waxyaabaha ka dhasha burburkan oo qor isla'egta nukliyeerka.
Dood:
Marka hore, waxaan aqoonsaneynaa in kaarboon-14 (\( ^{14}_{6}\text{C} \)) uu leeyahay tiro atom ah oo ah 6 iyo tiro cuf ah oo ah 14. Qallaf beta-ka yar, mid ka mid ah neutron-yada ku jira xudunta ayaa isu beddela proton. Tani waxay ka dhigan tahay in tirada atom ee xudunta ay kordho hal unug, halka tirada cufnadu ay isku mid tahay.
Waa kan isleegga burburka beta-min ee kaarboon-14:
\[
^{14}_{6}\qoraal{C} \rightarrow ^{14}_{7}\qoraal{N} + e^- + \bar{\nu}_e
\]
Halkee:
– Wax soo saarka qudhunku waa nitrogen-14 (\( ^{14}_{7}\text{N} \)).
– Elektaroonada (\( e^- \)) waa walxaha beta ee la sii daayo.
– \( \bar{\nu}_e \) waa elektaroono antineutrino ah oo sidoo kale la sii daayo.
Tusaale 2: Beta-plus Decay
Su'aal:
Nukliyeerka fluorine-18 (\( ^{18}_{9}\text{F} \)) wuxuu maraa burburka beta-plus. Go'aami waxyaabaha ka dhasha burburkan oo qor isla'egta nukliyeerka.
Dood:
Fluorine-18 (\( ^{18}_{9}\text{F} \)) waxay leedahay tiro atom ah oo ah 9 iyo tiro cuf ah oo ah 18. Qallaf beta-plus ah, proton-ka ku jira xudunta ayaa isu beddela neutron kaas oo tirada atomka hal mar hoos u dhigaya, laakiin tirada cufku way isku mid tahay.
Waa kan isle'egta burburka beta-plus ee fluorine-18:
\[
^{18}_{9}\qoraal{F} \rightarrow ^{18}_{8}\qoraal{O} + e^+ + \nu_e
\]
Halkee:
– Wax soo saarka qudhunku waa oksijiin-18 (\( ^{18}_{8}\text{O} \)).
– Positron (\( e^+ \)) waa walax beta ah oo la sii daayo.
– \( \nu_e \) waa elektaroono neutrino ah oo sidoo kale la soo saaro.
Su'aal Tusaale ah 3: Tamarta Burburka
Su'aal:
Xisaabi tamarta la sii daayo inta lagu jiro burburka beta-minus haddii isotope-ka strontium-90 (\( ^{90}_{38}\text{Sr} \)) uu u burburo yttrium-90 (\( ^{90}_{39}\text{Y} \)). Cufka strontium-90 waa 89,907738 u, cufka yttrium-90 waa 89,907152 u. Cufka elektaroonku waa 0,000548 u.
Dood:
Tamarta la sii daayo inta lagu jiro burburka beta-ka yar waxaa laga xisaabin karaa farqiga tirada ee u dhexeeya alaabada iyo falgalayaasha, ka dibna loo rogi karaa tamar iyadoo la adeegsanayo isla'egta Einstein \( E=mc^2 \).
Isbeddelka cufka (\( \Delta m \)) waa farqiga u dhexeeya cufka bilowga ah iyo cufka kama dambaysta ah, oo ay ku jiraan cufka elektaroonada la sii daayay:
\[
\Delta m = (\text{mass } ^{90}_{38}\text{Sr}) – (\text{mass } ^{90}_{39}\text{Y} + \text{electron mass})
\]
Beddelka qiimaha:
\[
\Delta m = 89,907738 \, \text{u} – (89,907152 \, \text{u} + 0,000548 \, \text{u})
\]
\[
\Delta m = 0,000038 \, \qoraal{u}
\]
Isbeddelka tirada ee tamarta loo beddelayo (1 u = 931.5 MeV/c²):
\[
E = \Delta m \times 931.5 \, \text{MeV/c}^2
\]
\[
E = 0,000038 \, \qoraal{u} \times 931.5 \, \qoraal{MeV}
\]
\[
E \ qiyaastii 0,03537 \, \qoraalka{MeV}
\]
Tamarta la sii daayo inta ay burburayso waa qiyaastii 0,03537 MeV.
Gabagabo
Qulqulka Beta waa dhacdo xiiso leh oo naga caawisa inaan fahanno isbeddellada qarsoon ee ka dhici kara gudaha nuclei-ga atomiga. Marka aan baranno qudhunka beta-minus iyo beta-plus, waxaan aqoonsan karnaa sida walxaha isu beddelaan walxo kale oo aan u xisaabinno tamarta la sii daayo inta lagu jiro hawsha. Iyada oo loo marayo dhibaatadan tusaalaha ah, waxaan helnaa aragti qoto dheer oo ku saabsan dhaqdhaqaaqa ku lug leh qudhunka shucaaca iyo muhiimadda fikradaha aasaasiga ah ee fiisigiska nukliyeerka.
