Ngā Tauira Pātai mō te Matapaki i te Ahupūngao Karihi me te Mahi Irahiko
Ko te ahupūngao karihi me te irahiko he peka o te ahupūngao e pā ana ki te ako i ngā karihi ngota me ngā āhuatanga pirau irahiko e puta ana i roto i ēnei karihi. He mea nui te mōhio ki ēnei ariā taketake i roto i ngā momo mara, tae atu ki te rongoā, te pūngao karihi, me te pūtaiao rauemi. I roto i tēnei tuhinga, ka matapakihia e mātou ētahi tauira raruraru e pā ana ki te ahupūngao karihi me te irahiko, me ō rātou whakamārama, hei āwhina i tō māramatanga.
He Kupu Whakataki Taketake ki te Ahupūngao Karihi me te Irahiko
I mua i te urunga atu ki ngā tauira pātai, he mea pai kia arotakehia ētahi ariā taketake:
– Te karihi ngota: Kei roto i tēnei ko ngā porotana me ngā irahiko. He pai te utu o ngā porotana, engari he kore utu ngā irahiko.
– Te mahi irahiko: Ko te tukanga pirau o ngā karihi kore pumau ki ngā karihi pumau ake mā te tukunga o ngā matūriki, te irahiko rānei.
– Ngā Momo Pirautanga Irahiko: Pirautanga Ārapa (\(\alpha\)), beta (\(\beta\)), me te gamma (\(\gamma\)).
– Te Ture o te Pirau Irahiko: E whakaahua ana i te hekenga o te maha o ngā karihi irahiko i roto i te wā.
Tauira Pātai 1: Te Papatipu me te Pūngao Pirau
Pātai:
Ka pirau te karihi uranium-238 hei thorium-234 mā te tukunga o tētahi matūriki ārepa. Mēnā ko te papatipu o te uranium-238 he 238.0508 u, ko te papatipu o te thorium-234 he 234.0436 u, ā, ko te papatipu o te matūriki ārepa he 4.0026 u, tatauhia te pūngao i tukuna i roto i tēnei pirau.
Kōrero:
Ka taea te tatau i te pūngao i tukuna i roto i te tukanga pirau mā te whakamahi i te whanaungatanga i waenga i te papatipu me te pūngao i homai e te whārite a Einstein \(E=mc^2\).
1. Tātaihia te papatipu e ngaro ana:
\( \Delta m = (papatipu_{U-238}) – (papatipu_{Th-234} + papatipu_{\alpha}) \)
\( = 238.0508 – (234.0436 + 4.0026) \)
\( = 238.0508 – 238.0462 \)
\( = 0.0046\, u \)
2. Tahurihia te papatipu ngaro ki te pūngao mā te whakamahi i te \( c^2 \):
\( E = \Delta m \times 931.5\, MeV/u \)
\( = 0.0046 \whakareatia 931.5 \)
\( \tata ki te 4.29\, MeV \)
Nō reira, ko te pūngao i tukuna i roto i tēnei pirau he tata ki te 4.29 MeV.
Tauira Pātai 2: Te Haurua-Ora me te Mahi
Pātai:
I te tīmatanga, ko te ngohe o tētahi tauira irahiko he 1000 Bq. I muri i ngā haora 10, ka heke tōna ngohe ki te 125 Bq. Tātaihia te haurua-ora o te matū irahiko.
Kōrero:
He rite tonu te mahi (A) o tētahi matū irahiko ki te maha o ngā karihi irahiko (N). E kī ana te ture o te pirau irahiko:
\[ A(t) = A_0 e^{-\lambda t} \]
Ko \( \lambda \) te pūmau pirau:
1. Tātaihia te pūmau pirau (\( \lambda \)):
\[ \frac{A(t)}{A_0} = e^{-\lambda t} \]
\[ \frac{125}{1000} = e^{-\lambda \times 10} \]
\[ 0.125 = e^{-\lambda \times 10} \]
\[ \ln(0.125) = -\lambda \whakanuia kia 10 \]
\[ \lambda = -\frac{\ln(0.125)}{10} \]
2. Whakatauhia te haurua-ora (\( T_{1/2} \)):
\[ T_{1/2} = \frac{\ln(2)}{\lambda} \]
\[ \lambda = \frac{\ln(8)}{10} = \frac{2.079}{10} = 0.2079 \, h^{-1} \]
\[ T_{1/2} = \frac{\ln(2)}{0.2079} \approx 3.3 \, hāora \]
Ko te haurua-ora o te matū irahiko e tata ana ki te 3.3 hāora.
Tauira 3: Te Pirau Beta me ngā Antineutrinos
Pātai:
Ka pirau te karihi Cobalt-60 mā te pirau beta-minus hei hanga i te karihi Nickel-60. Tuhia te tauhohenga karihi mō tēnei pirau, ka tautuhi i ngā matūriki e whai wāhi ana.
Kōrero:
Ka puta te pirau beta-minus (\(\beta^-\)) ina huri te neutron i roto i te karihi o te ngota hei proton, me te tuku i te irahiko (\(\beta^-\)) me te antineutrino (\(\bar{\nu}_e\)).
Ko te tauhohenga karihi mō tēnei pirau ko:
\[ _{27}^{60}Co \rightarrow _{28}^{60}Ni^ + e^- + \bar{\nu}_e \]
Kei hea:
– Ko \( _{27}^{60}Co \) ko Cobalt-60.
– Ko \( _{28}^{60}Ni^ \) he Nickel-60 kei roto i te āhua whakaohooho.
– He irahiko (pūmua beta-tango) a \( e^- \).
– Ko te \( \bar{\nu}_e \) he antineutrino.
Ko te nikara-60 i hangaia he maha ngā wā kei roto i te āhua whakaohooho, ā, ka tukuna atu he pūngao anō i roto i te āhua o ngā hihi gamma (\(\gamma\)) kia tae atu ai ki te āhua whenua. Ka taea te tuhi i te tauhohenga katoa penei:
\[ _{27}^{60}Co \rightarrow _{28}^{60}Ni + e^- + \bar{\nu}_e + \gamma \]
Tauira Pātai 4: Inenga Irahiko
Pātai:
Mena ka whakatakotoria he pūtake o te irahiko gamma me te ngohe o te 2 Curies ki te tawhiti o te 1 mita mai i tētahi mea, ā, ka mimitihia te irahiko e te mea mō te 5 meneti, tatauhia te horopeta irahiko i whiwhihia e te mea i roto i ngā rems. Me kī ko te nui o te irahiko i hipokina he 0.5 rad ia Curie ia meneti, ā, ko te tauwehenga kounga mō te irahiko gamma he 1.
Kōrero:
1. Tātaihia te horopeta i roto i te rad:
\[ \text{Horopeta (rad)} = \text{Te nui o te irahiko} \times \text{Mahi} \times \text{Wā (meneti)} \]
\[ = 0.5 \, rad/(Ci \cdot min) \times 2 \, Ci \times 5 \, min \]
\[ = 5 \, rād \]
2. Tātaihia te horopeta i roto i ngā parai:
\[ \text{Horopeta (rem)} = \text{Horopeta (rad)} \times \text{Tauwehe Kounga} \]
\[ = 5 \, rad \times 1 \, (mō te gamma) \]
\[ = 5 \, wareware \]
Ko te horopeta irahiko e whiwhihia ana e te mea he 5 rem.
Te Katinga
Mā te ako i ngā tauira rapanga i runga ake nei, ko te tumanako ka hōhonu ake tō māramatanga ki ngā ariā o te ahupūngao karihi me te mahi irahiko. He mea nui kia whakaharatauhia ngā rapanga rite tonu kia matatau ake ai koe ki te mārama me te whakamahi i ēnei ariā ahupūngao karihi. Kia pai tō ako!
