Ngā Tauira Pātai e Matapaki ana i te Pānga Whakaahua-Hiko
Ko te pānga hikohiko he āhuatanga ā-tinana e whakaahua ana i te tukunga o ngā irahiko mai i te mata o tētahi rauemi ina pā te mārama, te irahiko hikohiko rānei ki a ia. He mea nui te rangahau a Albert Einstein i te tīmatanga o te rautau 20 ki te whakamārama i tēnei āhuatanga, ā, i arahi atu ai ki te whakaae ki te ariā irahiko o te mārama. Ka matapakihia e tēnei tuhinga ētahi tauira raruraru e pā ana ki te pānga hikohiko me ngā whakamārama taipitopito mō ā rātou otinga.
Ariā Taketake
I mua i te neke atu ki ngā tauira raruraru, me arotake tātou i ētahi ariā taketake e pā ana ki te pānga hikohiko:
1. Pūngao photon: Ko te pūngao o te photon ka hoatuhia e te whārite \( E = h \nu \), ko \( h \) te pūmau a Planck (\( h \approx 6.626 \times 10^{-34} \) Js) ā, ko \( \nu \) te auau o te mārama.
2. Mahi (\( \phi \)): Ko te mahi te pūngao iti rawa e hiahiatia ana hei tango i ngā irahiko mai i te mata o te rauemi.
3. Pūngao nekeneke o ngā irahiko: Ko te pūngao nekeneke o ngā irahiko kua tukuna he rite ki te whārite \( KE = h \nu – \phi \).
Tauira Pātai 1
Pātai
Ko te mahi a te pepa whakarewa he \( 4.5 \) eV. Ka tiaho te mārama me te roanga ngaru o \( 200 \) nm ki runga i te pepa. Whakatauhia:
1. Te pūngao o te photon e mimitihia ana e te irahiko.
2. Ka tukuna ngā irahiko mai i te mata whakarewa?
3. Mena āe, he aha te pūngao nekeneke mōrahi o ngā irahiko kua tukuna?
Te Whakatau
1. Tātaihia te pūngao photon (\( E \))
\[
E = \frac{hc}{\lambda}
\]
Ko \( h \) te pūmau a Planck, ko \( c \) te tere o te mārama (\( c \approx 3 \times 10^8 \) m/s), ā, ko \( \lambda \) te roanga ngaru o te mārama.
\[
E = \frac{6.626 \times 10^{-34} \text{ Js} \times 3 \times 10^8 \text{ m/s}}{200 \times 10^{-9} \text{ m}}
\]
\[
E = \frac{1.9878 \times 10^{-25} \text{ Js}}{200 \times 10^{-9} \text{ m}}
\]
\[
E = 9.939 \times 10^{-19} \text{ J}
\]
Hei huri ki te eV, whakamahia \( 1 \text{ eV} = 1.602 \times 10^{-19} \text{ J} \).
\[
E = \frac{9.939 \times 10^{-19} \text{ J}}{1.602 \times 10^{-19} \text{ J/eV}}
\]
\[
E \tata ki te 6.2 \kuputuhi{ eV}
\]
2. Tirohia mēnā ka tukuna ngā irahiko
Nā te mea he nui ake te pūngao photon (6.2 eV) i te mahi (4.5 eV), ka tukuna te irahiko.
3. Tātaihia te pūngao nekeneke mōrahi o ngā irahiko
\[
KE = E – \phi = 6.2 \text{ eV} – 4.5 \text{ eV} = 1.7 \text{ eV}
\]
Tauira Pātai 2
Pātai
Ka tiaho te mārama me te auau o te \( 1.2 \times 10^{15} \) Hz ki runga i tētahi mata whakarewa he mahi mahi tōna o te \( 3 \) eV. Whakatauhia:
1. Te pūngao o te photon e mimitihia ana e te irahiko.
2. Ka tukuna ngā irahiko mai i te mata whakarewa?
3. Mena āe, he aha te pūngao nekeneke mōrahi o ngā irahiko kua tukuna?
Te Whakatau
1. Tātaihia te pūngao photon (\( E \))
\[
E = h \nu = 6.626 \times 10^{-34} \text{ Js} \times 1.2 \times 10^{15} \text{ Hz}
\]
\[
E = 7.9512 \times 10^{-19} \text{ J}
\]
Te tahuritanga ki te eV:
\[
E = \frac{7.9512 \times 10^{-19} \text{ J}}{1.602 \times 10^{-19} \text{ J/eV}}
\]
\[
E \tata ki te 4.97 \kuputuhi{ eV}
\]
2. Tirohia mēnā ka tukuna ngā irahiko
Nā te mea he nui ake te pūngao photon (4.97 eV) i te mahi (3 eV), ka tukuna te irahiko.
3. Tātaihia te pūngao nekeneke mōrahi o ngā irahiko
\[
KE = E – \phi = 4.97 \text{ eV} – 3 \text{ eV} = 1.97 \text{ eV}
\]
Tauira Pātai 3
Pātai
Ka pā te mārama UV me te roangaru o te \( 120 \) nm ki tētahi mata whakarewa he mahi mahi tōna \( 2.2 \) eV. Tātaihia:
1. Pūngao photon i roto i te eV.
2. Ka tukuna ngā irahiko mai i te mata whakarewa?
3. Mena āe, he aha te pūngao nekeneke mōrahi o ngā irahiko kua tukuna?
Te Whakatau
1. Tātaihia te pūngao photon (\( E \))
\[
E = \frac{hc}{\lambda}
\]
\[
E = \frac{6.626 \times 10^{-34} \text{ Js} \times 3 \times 10^8 \text{ m/s}}{120 \times 10^{-9} \text{ m}}
\]
\[
E = \frac{1.9878 \times 10^{-25} \text{ Js}}{120 \times 10^{-9} \text{ m}}
\]
\[
E = 1.6565 \times 10^{-18} \text{ J}
\]
Te tahuritanga ki te eV:
\[
E = \frac{1.6565 \times 10^{-18} \text{ J}}{1.602 \times 10^{-19} \text{ J/eV}}
\]
\[
E \tata ki te 10.34 \kuputuhi{ eV}
\]
2. Tirohia mēnā ka tukuna ngā irahiko
Nā te mea he nui ake te pūngao photon (10.34 eV) i te mahi (2.2 eV), ka tukuna te irahiko.
3. Tātaihia te pūngao nekeneke mōrahi o ngā irahiko
\[
KE = E – \phi = 10.34 \text{ eV} – 2.2 \text{ eV} = 8.14 \text{ eV}
\]
Whakamutunga
Ka taea te whakaatu i te āhuatanga pānga hikohiko mā roto i ngā tauira rapanga maha e tatau ai tātou i te kaha o te photon, e tirotiro ai mēnā ka taea te pana i te irahiko, me te ine i te kaha nekeneke mōrahi o te irahiko kua panaia. I te whakaoti rapanga, me tupato tātou ki ngā waeine ā-tinana me ngā huringa i waenga i ngā waeine (hei tauira, mai i ngā joule ki ngā electronvolts). Mā te māramatanga pakari me te mahi tika ka āwhina i a tātou ki te mōhio ki ngā ariā taketake o te pānga hikohiko, he pou nui tēnei o te ahupūngao matū.
