Ngā Tauira Pātai e Matapaki ana i ngā Koha Papatipu me te Pūngao Here
I roto i te ahupūngao karihi, he mea nui te mahi a ngā ariā o te hapa papatipu me te pūngao here ki te mārama ki te pumau o ngā karihi ngota. Ko te hapa papatipu e pā ana ki te rerekētanga i waenga i te papatipu tuturu o te karihi ngota me te papatipu katoa o ōna porotona me ngā niutoroneta. Ko tēnei whakamāramatanga e ahu mai ana i te māramatanga ka ngaro tetahi papatipu i te wā e hangaia ana te karihi, kātahi ka hurihia hei pūngao here e ai ki te mātāpono o te ōrite papatipu-pūngao i hangaia e Albert Einstein i roto i tana whārite rongonui, \(E=mc^2\).
Ko te pūngao here ko te nui o te pūngao e hiahiatia ana hei wehewehe i te karihi kia wehea ngā porotana me ngā niutara. Ko te nui ake o te pūngao here mō ia karihi, ko te pumau ake o te karihi. E whai ake nei he matapakinga mō ngā tauira raruraru e pā ana ki te hapa papatipu me te pūngao here hei whakahōhonu ake i tō tātou māramatanga ki tēnei ariā.
Tauira Pātai 1: Te Tatau i te Hapa Papatipu
Pātai:
Ka tonoa tētahi ākonga kia tatau i te hapa papatipu o te karihi ngota Hīriama-4 (\(^4_2He\)), e rua ngā porotana me rua ngā iōnitā. E mōhiotia ana ko te papatipu o te porotana he 1.007825 u, ko te papatipu o te iōnitā he 1.008665 u, ā, ko te papatipu o te karihi ngota Hīriama-4 he 4.002603 u. Tātaihia te hapa papatipu o te karihi.
Kōrero:
1. Whakatauhia te Papatipu Katoa o ngā Pūrotana me ngā Iūtorana:
Te maha o ngā porotini = 2, te maha o ngā niutorotini = 2
Papatipu katoa o ngā porotoni = 2 × 1.007825 u = 2.015650 u
Papatipu katoa o ngā niutron = 2 × 1.008665 u = 2.017330 u
Nō reira, ko te papatipu katoa o ngā porotona me ngā iōniutara ko:
\[
\text{Taumaha katoa} = 2.015650 \, \text{u} + 2.017330 \, \text{u} = 4.032980 \, \text{u}
\]
2. Te Tātai i te Hapa Papatipu:
\[
\text{Hapa Papatipu} (\Delta m) = \text{Papatipu Katoa} – \text{Papatipu Irahiko}
\]
\[
\Delta m = 4.032980 \, \text{u} – 4.002603 \, \text{u} = 0.030377 \, \text{u}
\]
Ko te papatipu hapa mō te karihi Hīriama-4 he 0.030377 u.
Tauira Pātai 2: Te Tatau i te Pūngao Here
Pātai:
Mā te whakamahi i te hapa papatipu mai i te tauira tuatahi, tatauhia te pūngao here o te karihi Hīriama-4. (E whakaatu ana: 1 u = 931.5 MeV/c²)
Kōrero:
1. Te Tahuri i te Hapa Papatipu ki te Pūngao:
Ka tatauhia te pūngao here (\(E\)) mā te whakamahi i te whārite \(E = \Delta m \times c^2\). I konei, ko \(c^2\) i roto i ngā waeine e whakamahia whānuitia ana o MeV/u ko 931.5 MeV/u.
\[
E = 0.030377 \, \text{u} \times 931.5 \, \text{MeV/u}
\]
\[
E = 28.299 \, \text{MeV}
\]
Ko te pūngao here o te karihi Hīriama-4 he 28.299 MeV.
2. Te Tātai i te Pūngao Herea mō ia Nucleon:
E 4 ngā nucleon katoa o te Hīriamu-4 (2 ngā porotoni me 2 ngā niutironi). Hei kimi i te pūngao here mō ia nucleon, ka wehea e mātou te pūngao here katoa mā te maha o ngā nucleon:
\[
\text{Pūngao here mō ia irahiko} = \frac{28.299 \, \text{MeV}}{4} = 7.075 \, \text{MeV/irahiko}
\]
Ngā Ariā Matatau
He mea nui te mārama ki te pūngao here mō ia nucleon hei whakatau i te pumau o te karihi; ki te teitei ake tēnei uara, ka pumau ake te karihi. Ko ngā karihi he nui te pūngao here mō ia nucleon ka ātete ake ki ngā tauhohenga pēnei i te wehenga, te hanumi rānei.
Tauira Pātai 3: Te Whakataurite i te Pūngao Here
Pātai:
Whakatauritea te pūngao here mō ia karihiona mō ngā karihi ngota e rua e whai ake nei: Deuterium (\(^2_1H\)) me te papatipu karihi o te 2.014102 u me te Hēriuma-4 mai i te tauira o mua, ka tatau i te rerekētanga. Ko te papatipu o te pūrotene he 1.007825 u, ā, ko te papatipu o te niutron he 1.008665 u.
Kōrero:
1. Teuterium (\(^2_1H\)):
– Te Papatipu Katoa o ngā Pūrotana me ngā Neutron:
Papatipu katoa = 1 × 1.007825 u + 1 × 1.008665 u = 2.016490 u
– Te Koha o te Papatipu Deuterium:
\[
\Delta m = 2.016490 \, \text{u} – 2.014102 \, \text{u} = 0.002388 \, \text{u}
\]
– Pūngao Here Deuterium:
\[
E = 0.002388 \, \text{u} \times 931.5 \, \text{MeV/u} = 2.223 \, \text{MeV}
\]
– Pūngao Here mō ia Deuterium Nucleon:
Nā te mea e rua ngā nucleon o te Deuterium (1 te porotoni me te 1 te niutironi),
\[
\frac{2.223 \, \text{MeV}}{2} = 1.1115 \, \text{MeV/karukeona}
\]
2. Whakataurite me te Whakamutunga:
Pūngao here mō ia nucleon o te Hēriuma-4: 7.075 MeV/nucleon
Pūngao here mō ia nucleon o Deuterium: 1.1115 MeV/nucleon
Rerekētanga:
\[
7.075 \, \text{MeV/karukeona} – 1.1115 \, \text{MeV/karukeona} = 5.9635 \, \text{MeV/karukeona}
\]
Mai i tēnei whakataurite, ka kite tātou he tino pumau ake te Hēriuma-4 i te Deuterium, e tohuhia ana e tōna pūngao here teitei ake mō ia nukleona.
Whakamutunga
He mea nui te mārama ki te hapa papatipu me te pūngao here i roto i te ahupūngao karihi, ā, ka homai he māramatanga ki te pumau o te karihi. Mā te tatau i te pūngao here, ka taea e tātou te matapae i te tauhohenga me te pumau o ētahi isotopes. Ehara i te mea he mea taketake noa iho ēnei ariā ki te ahupūngao ariā engari he tono mahi anō hoki, tae atu ki te whakaputa mana karihi me te rangahau whetū. Mā te mahi i ngā raruraru pēnei i ngā mea o runga ake nei, ka pai ake tō tātou kaha ki te mārama me te whakamahi i ēnei ariā uaua.
