Ngā Tauira Pātai e Matapaki ana i te Auahatanga Ianuma me te Ariā Atomika
He peka nui te miihini irahiko o te ahupūngao e ako ana i te hanganga me te whanonga o ngā ngota i runga i ngā mātāpono o te miihini irahiko. He mea nui te mārama ki tēnei ariā mō ngā ākonga me ngā tohunga mātauranga e whai wāhi ana ki te ahupūngao, te matū, me te pūtaiao rauemi. Ko te whāinga o tēnei tuhinga he whakarato i ngā tauira rapanga me ā rātou matapakinga mō te miihini irahiko hei āwhina i ngā kaipānui ki te mōhio ki ngā ariā matua o tēnei kaupapa.
He Kupu Whakataki ki te Āhuahanga Ianuma, te Ariā Atomika
I whakawhanakehia te ariā miihini irahiko o te ngota i te tīmatanga o te rautau 20 i te tīmatanga o te kitenga o ngā kaipūtaiao kāore te tauira ngota tawhito i te rawaka hei whakamārama i ngā āhuatanga rerekē i kitea i roto i ngā whakamātautau. Ko tētahi o ngā whakatutukitanga nui i roto i te whanaketanga o tēnei ariā ko te tauira ngota Bohr, i muri mai ka whakatikatikaina, ka tino pai ake hoki ki te ariā miihini ngaru a Schrödinger me te mātāpono koretake a Heisenberg.
I te nuinga o te wā, e whakamārama ana te ariā ngota ngota matūriki kāore ngā irahiko e karapoti ana i te karihi ngota e noho ana i roto i ngā porowhita pumau pērā i ngā aorangi e karapoti ana i te rā, engari i roto i ngā porowhita – ngā rohe i te wāhi e teitei ana te tūponotanga o te kitea o tētahi irahiko. Ka whakaahuahia ēnei porowhita e ngā mahi ngaru i ahu mai i te whārite Schrödinger.
Ngā Tauira Pātai me te Kōrero:
Pātai 1: Whirihoranga Irahiko
Pātai:
Whakatauhia te whirihoranga irahiko mō te ngota hāora (Z = 8) mā te whakamahi i te mātāpono Aufbau, te mātāpono a Pauli, me te ture a Hund.
Kōrero:
Hei whakatau i te whirihoranga irahiko o te Hāora me te tau ngota 8, ka whakamahia e mātou te mātāpono Aufbau e kī ana ko ngā irahiko ka whakakī i ngā porowhita mai i te taumata pūngao iti rawa i te tuatahi.
Ngā Hipanga:
1. Te Mātāpono Aufbau:
– Ka whakakīia ngā porowhita i runga i te raupapatanga o te pūngao: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, me ērā atu.
2. Te mātāpono a Pauli:
– Ka taea anake te whakakī i ia porowhita e ngā irahiko e rua me ngā takahuri rerekē.
3. Te Ture a Hund:
– Ka whakakīia ngā porowhita e ngā irahiko ki te pūngao ōrite i te wā whakarara i mua i te hononga.
Te whirihoranga irahiko mō te Hāora:
– E waru ngā irahiko o te hāora.
– Ka taea e te 1s te pupuri i ngā irahiko e 2: 1s²
– Ka taea hoki e te 2s te pupuri i ngā irahiko e 2: 2s²
– E ono ngā irahiko ka taea e te 2p te pupuri, engari e whā noa iho ngā irahiko e toe ana i te Hāora.
Nō reira, ko te whirihoranga irahiko mō te Hāora ko 1s² 2s² 2p⁴.
Pātai 2: Te Mātāpono o te Āhua Korekore a Heisenberg
Pātai:
Tātaihia te koretake o te tūranga (Δx) o tētahi irahiko mēnā e mōhiotia ana ko te koretake o te nekehanga (Δp) o te irahiko he 2.5 x 10^-24 kg m/s.
Kōrero:
E ai ki te Mātāpono Koretake a Heisenberg, kāore e taea te mōhio tika me te wā kotahi ki te tūranga me te nekehanga o tētahi matūriki. Mā te pāngarau, e kīia ana penei:
\[ \Delta x \cdot \Delta p \ge \frac{h}{4\pi} \]
Kei hea:
– Ko te \( \Delta x \) te koretake o te tūnga,
– Ko te koretake o te nekehanga \( \Delta p \)
– Ko te pūmau a Planck ko te \( h \) (6.626 x 10^-34 Js).
E mōhiotia ana:
\[ \Delta p = 2.5 \times 10^{-24} \; \text{kg m/s} \]
Nā, ka taea e tātou te tatau:
\[ \Delta x \ge \frac{h}{4\pi \Delta p} = \frac{6.626 \times 10^{-34}}{4 \pi \times 2.5 \times 10^{-24}} \]
\[ \Delta x \ge \frac{6.626 \times 10^{-34}}{3.14 \times 10^{-23}} \]
\[ \Delta x \ge 2.10 \times 10^{-11} \; \text{m} \]
Nō reira, ko te koretake o te tūranga o te irahiko e tata ana ki te \( 2.10 \times 10^{-11} \; \text{m} \).
Pātai 3: Ngā Mahi Ngaru me ngā Āmiotanga
Pātai:
Whakaahuahia te āhua me te takotoranga o te porowhita 2p, ā, homai ōna tau irahiko.
Kōrero:
Ko te porowhita 2p tētahi o ngā porowhita e toru i roto i te anga iti p (px, py, pz). He āhua motuhake tō tēnei porowhita e rite ana ki te dumbbell, ki ngā poihau e rua rānei e hono ana i waenganui.
E toru ngā aronga motuhake o ia porowhita-p i te wāhi, e rite ana ki ngā tuaka taunga x, y, me z, e mōhiotia ana ko px, py, me pz. Ka tautuhia ia aronga e te tau irahiko aukume ml, e taea ai te tango i ngā uara -1, 0, +1 rānei mō te anga iti-p.
Ko ngā tau irahiko e pā ana ki te porowhita 2p ko:
– Tau Irahiko Matua (n): 2 (e tohu ana kei te taumata pūngao tuarua te irahiko)
– Tau Irahiko Azimuthal (l) : 1 (e tohu ana i te porowhita p)
– Tau Ianuku Aukume (ml): -1, 0, +1 (e tohu ana i te aronga i te wāhi)
Nō reira, e toru ngā āhua ōrite o te porowhita 2p me ngā whakatakotoranga rerekē e ai ki te uara ml.
Whakamutunga
Kei roto i tēnei tuhinga ētahi tauira raruraru me ngā kōrero mō te ariā ngota ngota. Ka hipokina e tēnei mahi te whirihoranga irahiko, te mātāpono koretake o Heisenberg, me te āhua me te whakatakotoranga o ngā porowhita. He mea nui te mārama ki ēnei ariā hei whakahaere i ngā kaupapa matua o te ngota ngota e pā ana ki te hanganga ngota. Mā te mahi auau me te kōrero mō ngā raruraru, ko te tumanako ka māmā ake te mārama me te whakamahi i ngā mātāpono o te ngota ngota i roto i ngā horopaki pūtaiao rerekē.
