Ngā Tauira Pātai e Matapaki ana i te Ariā o ngā Photon
Ko ngā photon he matūriki taketake e hanga ana i te pūtake o te ariā irahiko o te mārama. Hei irahiko o te mārama, ka mau te photon i tētahi putea pūngao e pā tika ana ki tōna auau. I whakaurua tuatahitia tēnei ariā e Albert Einstein i te tau 1905. I roto i tēnei tuhinga, ka matapakihia e mātou ētahi tauira me ngā kōrero mō ngā photon hei whakamārama i tō mātou māramatanga ki tēnei kaupapa.
Te Māramatanga Taketake o ngā Photon
Ko ngā photon he matūriki māmā, he quanta rānei, o te irahiko hikohiko. I roto i te ariā kuantum, kāore he papatipu okiokinga o ngā photon engari he pūngao me te nekehanga kei a rātou. Ka taea te tatau i te pūngao o te photon mā te whakamahi i te whārite i whakawhanakehia e Max Planck:
\[ E = hf \]
Dimana:
– Ko te pūngao photon te \( E \)
– Ko te pūmau a Planck te \( h \) ( \( 6.626 \times 10^{-34} \) Js)
– Ko te auau o te māramatanga ko \( f \)
Ka taea te whakaatu i te whanaungatanga i waenga i te pūngao photon me te roanga ngaru \(\lambda\) mā te whārite e whai ake nei:
\[ E = \frac{hc}{\lambda} \]
Dimana:
– Ko te tere o te mārama i roto i te korehau \( c \) \( (3 \times 10^8 \) m/s)
Ngā Pātai Tauira me te Kōrero
Pātai 1: Te Tatau i te Pūngao Photon
Pātai: Ko te roanga ngaru o te photon he 500 nm. Tātaihia te pūngao o te photon i roto i ngā joule.
Kōrero:
Tuatahi, ka hurihia e tātou te roanga ngaru mai i ngā nanometer ki ngā mita.
\[ 500 \ \kuputuhi{nm} = 500 \times 10^{-9} \ \kuputuhi{m} \]
Mā te whakamahi i te whārite pūngao photon:
\[ E = \frac{hc}{\lambda} \]
Whakauruhia ngā uara o te pūmau a Planck ( \( h = 6.626 \times 10^{-34} \) Js) me te tere o te mārama \( c = 3 \times 10^8 \ \text{m/s} \):
\[ E = \frac{(6.626 \times 10^{-34} \ \text{Js}) \times (3 \times 10^8 \ \text{m/s})}{500 \times 10^{-9} \ \text{m}} \]
\[ E = \frac{1.9878 \times 10^{-25}}{500 \times 10^{-9}} \]
\[ E = 3.976 \times 10^{-19} \ \text{J} \]
Nō reira, ko te pūngao o te photon ko \( 3.976 \times 10^{-19} \) joules.
Pātai 2: Te Tātai i te Auautanga o te Pūngao Photon
Pātai: Mena he \( 2.5 \times 10^{-19} \) joules te kaha o te photon, he aha te auau o te māramatanga o taua photon?
Kōrero:
Ka whakamahia e mātou te whārite taketake o te pūngao photon:
\[ E = hf \]
Ka wehea e mātou te auau \( f \):
\[ f = \frac{E}{h} \]
Whakauruhia ngā uara o te pūngao \( E \) me te pūmau a Planck \( h \):
\[ f = \frac{2.5 \times 10^{-19} \ \text{J}}{6.626 \times 10^{-34} \ \text{Js}} \]
\[ f = 3.77 \times 10^{14} \ \text{Hz} \]
Nō reira, ko te auau o te mārama ko \( 3.77 \times 10^{14} \ \text{Hz} \).
Pātai 3: Pānga Whakaahua-Hiko
Pātai: I roto i tētahi whakamātautau pānga hikohiko, ka pā tētahi photon me te pūngao 4.0 eV ki tētahi mata whakarewa, ka tukuna he irahiko. Mena ko te mahi a te whakarewa he 2.5 eV, tatauhia te pūngao nekeneke mōrahi o te irahiko i tukuna.
Kōrero:
Ko te pūngao photon \( E \) e hoatu ana i roto i ngā electronvolts (eV). Ka taea e tātou te whakamahi tika i tēnei uara nā te mea kei roto hoki te mahi i roto i te eV.
Ko te mahi mahi (\( W \)) te pūngao iti rawa e hiahiatia ana hei tango i tētahi irahiko mai i te mata whakarewa. Ko te pūngao nekeneke mōrahi (\( KE \)) o tētahi irahiko ka tatauhia hei rerekētanga i waenga i te pūngao photon me te mahi mahi:
\[ KE = E – W \]
Whakauruhia ngā uara o te pūngao photon \( E = 4.0 \ \text{eV} \) me te mahi \( W = 2.5 \ \text{eV} \):
\[ KE = 4.0 \ \text{eV} – 2.5 \ \text{eV} \]
\[ KE = 1.5 \ \text{eV} \]
Nō reira, ko te pūngao nekeneke mōrahi o te irahiko i tukuna ko 1.5 eV.
Pātai 4: Te Roanga Ngaru Mai i te Auautanga
Pātai: He aha te roanga ngaru o te photon he auau o \( 6 \times 10^{14} \ \text{Hz} \)?
Kōrero:
Mā te whakamahi i te whanaungatanga i waenga i te tere o te mārama, te auau, me te roanga ngaru:
\[ c = \lambda f \]
Ka wehea e mātou te roanga ngaru \( \lambda \):
\[ \lambda = \frac{c}{f} \]
Tāuruhia ngā uara mō te tere o te mārama \( c = 3 \times 10^8 \ \text{m/s} \) me te auau \( f = 6 \times 10^{14} \ \text{Hz} \):
\[ \lambda = \frac{3 \times 10^8 \ \text{m/s}}{6 \times 10^{14} \ \text{Hz}} \]
\[ \lambda = 5 \times 10^{-7} \ \text{m} \]
\[ \lambda = 500 \ \kuputuhi{nm} \]
Nō reira, ko te roanga ngaru o te photon he 500 nm.
Pātai 5: Te Pūngao Photon i roto i te Whānuitanga
Pātai: Ko te roanga ngaru o te photon i roto i te whānuitanga ultraviolet he 150 nm. Tātaihia te pūngao o te photon i roto i ngā joule me ngā electronvolts.
Kōrero:
Tuatahi, hurihia te roanga ngaru ki ngā mita:
\[ 150 \ \kuputuhi{nm} = 150 \times 10^{-9} \ \kuputuhi{m} \]
Te tatau i te pūngao photon i roto i ngā joule:
\[ E = \frac{hc}{\lambda} \]
Whakauruhia ngā uara:
\[ E = \frac{(6.626 \times 10^{-34} \ \text{Js}) \times (3 \times 10^8 \ \text{m/s})}{150 \times 10^{-9} \ \text{m}} \]
\[ E = \frac{1.9878 \times 10^{-25}}{150 \times 10^{-9}} \]
\[ E = 1.3252 \times 10^{-18} \ \text{J} \]
Hei huri i ngā joule ki ngā electronvolts, ka whakamahia e mātou te 1eV = \( 1.602 \times 10^{-19} \) J:
\[ E \ (\text{eV}) = \frac{1.3252 \times 10^{-18} \ \text{J}}{1.602 \times 10^{-19} \ \text{J/eV}} \]
\[ E \ (\text{eV}) = 8.27 \ \text{eV} \]
Nō reira, ko te pūngao o te photon ultraviolet ko \( 1.3252 \times 10^{-18} \ \text{J} \) ko 8.27 eV rānei.
Whakamutunga
Mai i ngā tauira raruraru me ngā kōrero i runga ake nei, kua ruku hohonu tātou ki ngā āhuatanga me ngā tātaitanga e pā ana ki ngā photon. Kei roto i tēnei ko te tātai i te pūngao i runga i te roangaru me te auau, tae atu ki te whakamahinga o te ariā photon i roto i te pānga photoelectric. He mea nui te mārama ki te ariā photon ehara i te mea i roto i te ahupūngao ariā anake engari i roto hoki i ngā tono hangarau hou pērā i te photovoltaics, te lasers, me ngā pūoko mārama. Mēnā he nui te mahi, ka māmā ake, ka māmā ake te mārama ki ēnei ariā.
