Su'aalo Tusaale ah oo Ka Hadlaya Cilladaha Culus iyo Tamarta Isku Xidhnaanta
Fiisigiska nukliyeerka, fikradaha cilladda cufka iyo tamarta isku xidhka ayaa door muhiim ah ka ciyaara fahamka xasilloonida nucleus-ka atomiga. Cilladda cufka waxay tilmaamaysaa farqiga u dhexeeya cufka dhabta ah ee nucleus-ka atomiga iyo cufka guud ee proton-yada iyo neutron-yada ay ka kooban tahay. Qeexitaankani wuxuu ku salaysan yahay fahamka in cuf qaar uu lumo inta lagu jiro sameynta nucleus, kaas oo markaa loo beddelo tamar isku xidhka iyadoo la raacayo mabda'a isku dheelitirka cufka iyo tamarta ee uu Albert Einstein ku sameeyay isla'egtiisa caanka ah, \(E=mc^2\).
Tamarta isku xidhka waa xaddiga tamarta loo baahan yahay si loo kala qaybiyo bu'da una kala qaybiyo protons iyo neutrons-yo kala duwan. Inta badan tamarta isku xidhka bu'da kasta, ayaa xudunta sii xasilloon. Kuwa soo socdaa waa dood ku saabsan tusaale ahaan dhibaatooyinka la xiriira cilladda tirada iyo tamarta isku xidhka si loo qotomiyo fahamkeenna fikraddan.
Su'aal Tusaale ah 1: Xisaabinta Cilladaha Cufnaanta
Su'aal:
Arday ayaa la weydiisanayaa inuu xisaabiyo cilladda cufka ee xudunta atomiga Helium-4 (\(^4_2He\)), oo ka kooban 2 protons iyo 2 neutrons. Waxaa la ogyahay in cufka proton uu yahay 1.007825 u, cufka neutron-ku waa 1.008665 u, cufka xudunta atomiga Helium-4 waa 4.002603 u. Xisaabi cilladda cufka ee xudunta.
Dood:
1. Go'aami Wadarta Cufka Borotoonada iyo Niyuutaroonada:
Tirada borotoonnada = 2, tirada niyuutaroonnada = 2
Wadarta cufka protons = 2 × 1.007825 u = 2.015650 u
Wadarta cufka neutroonada = 2 × 1.008665 u = 2.017330 u
Sidaa darteed, wadarta guud ee protons iyo neutrons waa:
\[
\text{Wadarta cufnaanta} = 2.015650 \, \text{u} + 2.017330 \, \text{u} = 4.032980 \, \text{u}
\]
2. Xisaabinta Cilladaha Cufnaanta:
\[
\text{Cillad Culus} (\Delta m) = \text{Wadarta Culayska} – \text{Culayska Nukliyeerka}
\]
\[
\Delta m = 4.032980 \, \text{u} – 4.002603 \, \text{u} = 0.030377 \, \text{u}
\]
Cilladda cufka ee xudunta Helium-4 waa 0.030377 u.
Su'aal Tusaale 2: Xisaabinta Tamarta Isku Xidhnaanta
Su'aal:
Adigoo isticmaalaya cilladda cufnaanta ee ka timid dhibaatada tusaalaha koowaad, xisaabi tamarta isku xidhka ee xudunta Helium-4. (Marka la eego: 1 u = 931.5 MeV/c²)
Dood:
1. U beddelashada cilladda cufnaanta tamarta tamarta:
Tamarta isku xidhka (\(E\)) waxaa lagu xisaabiyaa iyadoo la adeegsanayo isleegga \(E = \Delta m \times c^2\). Halkan, \(c^2\) ee cutubyada caadiga ah ee MeV/u waa 931.5 MeV/u.
\[
E = 0.030377 \, \text{u} \times 931.5 \, \text{MeV/u}
\]
\[
E = 28.299 \, \qoraal{MeV}
\]
Tamarta isku xidhka ee xudunta Helium-4 waa 28.299 MeV.
2. Xisaabinta Tamarta Isku Xidhnaanta Nukliyeerkiiba:
Helium-4 wuxuu leeyahay wadarta guud ee 4 nukliyeer (2 protons iyo 2 niyuutrooni). Si loo helo tamarta isku xidhka halkii nukliyeer, waxaan tamarta isku xidhka guud u qaybinaynaa tirada nukliyeerada:
\[
\text{Tamarta isku xidhka halkii nukliyeer} = \frac{28.299 \, \text{MeV}}{4} = 7.075 \, \text{MeV/nukliyeon}
\]
Fikradaha Sare
Fahmidda tamarta isku xidhka ee nukliyeer kasta waa muhiim si loo go'aamiyo xasilloonida nukliyeerka; qiimahaas oo kordha, ayaa nukliyeerku sii xasilloonaan doonaa. Nukliyeerka leh tamar isku xidhka sare ee nukliyeer kasta wuxuu u janjeeraa inuu u adkaysto falcelinta sida kala-goynta ama isku-dhafka.
Su'aal Tusaale ah 3: Isbarbardhigga Tamarta Isku Xiran
Su'aal:
Isbarbardhig tamarta isku xidhka nukliyeerkiiba labada nukliyeer ee soo socda: Deuterium (\(^2_1H\)) oo leh cuf nukliyeer ah oo ah 2.014102 u iyo Helium-4 oo laga soo qaatay tusaalihii hore, oo xisaabi faraqa. Cufnaanta proton-ku waa 1.007825 u cufnaanta neutron-kuna waa 1.008665 u.
Dood:
1. Deuterium (\(^2_1H\)):
– Wadarta Cufnaanta Borotoonnada iyo Niyuutaroonnada:
Wadarta cufka = 1 × 1.007825 u + 1 × 1.008665 u = 2.016490 u
- Cilladda Cufka ee Deuterium:
\[
\Delta m = 2.016490 \, \text{u} – 2.014102 \, \text{u} = 0.002388 \, \text{u}
\]
- Tamarta Xidhitaanka Deuterium:
\[
E = 0.002388 \, \text{u} \times 931.5 \, \text{MeV/u} = 2.223 \, \text{MeV}
\]
- Tamarta isku xidhka Nukliyeerka Deuterium:
Sababtoo ah Deuterium wuxuu leeyahay 2 nukliyeer (1 proton iyo 1 neutron),
\[
\frac{2.223 \, \text{MeV}}{2} = 1.1115 \, \text{MeV/nucleon}
\]
2. Isbarbardhigga iyo Gunaanadka:
Tamarta isku xidhka halkii nukliyeer ee Helium-4: 7.075 MeV/nukliyeer
Tamarta isku xidhka halkii nukliyeer ee Deuterium: 1.1115 MeV/nukliyeer
Farqiga:
\[
7.075 \, \qoraalka{MeV/nucleon} – 1.1115 \, \qoraalka{MeV/nucleon} = 5.9635 \, \qoraalka{MeV/nucleon}
\]
Marka la barbardhigo, waxaan arki karnaa in Helium-4 uu aad uga xasilloon yahay Deuterium, sida lagu muujiyay tamartiisa isku xidhka ee aadka u sarreysa ee nukliyeer kasta.
Gabagabo
Fahmidda cilladda tirada iyo tamarta isku xidhka ayaa muhiim u ah fiisigiska nukliyeerka waxayna bixisaa aragti ku saabsan xasilloonida nukliyeerka. Marka la xisaabiyo tamarta isku xidhka, waxaan saadaalin karnaa falcelinta iyo xasilloonida isotopes-ka qaarkood. Fikradahani ma aha oo kaliya aasaaska fiisigiska aragtida laakiin sidoo kale waxay leeyihiin codsiyo wax ku ool ah, oo ay ku jiraan soo saarista tamarta nukliyeerka iyo cilmi-baarista xiddigiska. Marka la kulmao dhibaatooyinka sida kuwa kor ku xusan, awooddeenna aan ku fahmi karno oo aan ku dabaqi karno fikradahan adag ayaa fiicnaan doonta.
