Ngā Tauira Pātai e Matapaki ana i te Pūngao Ngaru Hikohiko
He mea nui te pūngao ngaru hikohiko i roto i te whānuitanga o ngā tono hangarau me te pūtaiao. Mai i ngā whakawhitiwhiti kōrero reo irirangi ki ngā hihi-X hauora, he mea nui te mārama ki ngā ngaru hikohiko me ō rātou pūngao. Ka kapi i tēnei tuhinga ngā ariā matua me te whakarato i ngā tauira rapanga mō te pūngao ngaru hikohiko, e kapi ana i ngā āhuatanga ariā me ngā āhuatanga mahi.
He Kupu Whakataki ki ngā Ngaru Hikohiko
Ko ngā ngaru hikohiko he ngaru e tito ana i ngā papa hiko me ngā papa aukume e wiri ana, e haere ana i te wāhi i te tere o te mārama. Ka puta mai ēnei mā te huri haere o ngā papa hiko me ngā papa aukume, ā, ka taea te horapa mā te korehau, mā roto rānei i ngā rauemi. Kei roto i te whānuitanga o ngā ngaru te whānuitanga o ngā ngaru, mai i ngā ngaru reo irirangi he roa ngā roangaru ki ngā hihi gamma he poto rawa ngā roangaru.
I te nuinga o te wā, ka taea te whakaatu i te kaha o ngā ngaru hikohiko i roto i te āhua o tētahi whārite:
\[ E = h \cdot f \]
Ko \( E \) te pūngao photon, ko \( h \) te pūmau Planck (\(6.626 \times 10^{-34} \, \text{Js} \)), ā, ko \( f \) te auau ngaru. Mā te mōhio ki te auau, ki te roanga ngaru rānei (\( \lambda \)), ka taea e tātou te tatau i te pūngao o te ngaru hikohiko mā te whakamahi i te tere o te mārama (\( c = 3 \times 10^8 \, \text{m/s} \)), ko \( c = \lambda \cdot f \).
Tauira Pātai 1
Pātai:
Ko te auau o tētahi ngaru hikohiko he \( 5 \times 10^{14} \, \text{Hz} \). Tātaihia te pūngao o te kotahi photon o tēnei ngaru hikohiko.
Kōrero:
Whakamahia te whārite \( E = h \cdot f \):
\[ h = 6.626 \times 10^{-34} \, \text{Js} \]
\[ f = 5 \times 10^{14} \, \text{Hz} \]
Nō reira,
\[ E = (6.626 \times 10^{-34} \, \text{Js}) \cdot (5 \times 10^{14} \, \text{Hz}) \]
\[ E = 3.313 \times 10^{-19} \, \text{J} \]
Ko te pūngao o te kotahi photon o te ngaru hikohiko ko \( 3.313 \times 10^{-19} \, \text{J} \).
Tauira Pātai 2
Pātai:
Mena he roangaru te roangaru o te hihi \( \lambda \) o \( 600 \, \text{nm} \), tatauhia tōna pūngao mō ia photon i roto i ngā irahiko hiko (eV). (Kua hoatu: 1 eV = \( 1.602 \times 10^{-19} \, \text{J} \)).
Kōrero:
Tuatahi, hurihia te roangaru kua hoatu ki ngā mita:
\[ \lambda = 600 \, \text{nm} = 600 \times 10^{-9} \, \text{m} \]
Whakamahia te whanaungatanga \( c = \lambda \cdot f \) hei kimi i te auau:
\[ c = 3 \whakareatia ki te 10^8 \, \kuputuhi{m/s} \]
\[ f = \frac{c}{\lambda} = \frac{3 \times 10^8 \, \text{m/s}}{600 \times 10^{-9} \, \text{m}} \]
\[ f = 5 \times 10^{14} \, \text{Hz} \]
Nā, tatauhia te pūngao photon mā te whakamahi i te \( E = h \cdot f \):
\[ h = 6.626 \times 10^{-34} \, \text{Js} \]
\[ E = (6.626 \times 10^{-34} \, \text{Js}) \cdot (5 \times 10^{14} \, \text{Hz}) \]
\[ E = 3.313 \times 10^{-19} \, \text{J} \]
Inaianei, hurihia te pūngao ki ngā ngaohiko irahiko:
\[ E = \frac{3.313 \times 10^{-19} \, \text{J}}{1.602 \times 10^{-19} \, \text{J/eV}} \]
\[ E \tata ki te 2.07 \, \text{eV} \]
Nō reira, ko te pūngao mō ia photon o te irahiko me te roangaru \( 600 \, \text{nm} \) he tata ki te 2.07 eV.
Tauira Pātai 3
Pātai:
Ko te roanga ngaru o ngā ngaruiti he \( 12 \, \text{cm} \). Tātaihia te kaha o te kotahi photon o tēnei ngaruiti.
Kōrero:
Tuatahi, hurihia te roangaru kua hoatu ki ngā mita:
\[ \lambda = 12 \, \kuputuhi{cm} = 12 \times 10^{-2} \, \kuputuhi{m} \]
Whakamahia te whanaungatanga \( c = \lambda \cdot f \) hei kimi i te auau:
\[ c = 3 \whakareatia ki te 10^8 \, \kuputuhi{m/s} \]
\[ f = \frac{c}{\lambda} = \frac{3 \times 10^8 \, \text{m/s}}{12 \times 10^{-2} \, \text{m}} \]
\[ f = 2.5 \times 10^9 \, \text{Hz} \]
Nā, tatauhia te pūngao photon mā te whakamahi i te \( E = h \cdot f \):
\[ h = 6.626 \times 10^{-34} \, \text{Js} \]
\[ E = (6.626 \times 10^{-34} \, \text{Js}) \cdot (2.5 \times 10^9 \, \text{Hz}) \]
\[ E = 1.6565 \times 10^{-24} \, \text{J} \]
Ko te pūngao o te kotahi photon o ngā ngaruiti me te roanga ngaru \( 12 \, \text{cm} \) ko \( 1.6565 \times 10^{-24} \, \text{J} \).
Tauira Pātai 4
Pātai:
Tātaihia te maha o ngā photon i hangaia e te laser me te mana \( 1 \, \text{W} \) e tuku ana i te mārama me te roangaru \( 500 \, \text{nm} \) mō \( 1 \, \text{s} \).
Kōrero:
Tuatahi, tatauhia te pūngao o tētahi photon kotahi me te roangaru \( 500 \, \text{nm} \):
\[ \lambda = 500 \, \text{nm} = 500 \times 10^{-9} \, \text{m} \]
Whakamahia te whanaungatanga \( c = \lambda \cdot f \) hei kimi i te auau:
\[ c = 3 \whakareatia ki te 10^8 \, \kuputuhi{m/s} \]
\[ f = \frac{c}{\lambda} = \frac{3 \times 10^8 \, \text{m/s}}{500 \times 10^{-9} \, \text{m}} \]
\[ f = 6 \times 10^{14} \, \text{Hz} \]
Mā te whakamahi i te \( E = h \cdot f \):
\[ h = 6.626 \times 10^{-34} \, \text{Js} \]
\[ E = (6.626 \times 10^{-34} \, \text{Js}) \cdot (6 \times 10^{14} \, \text{Hz}) \]
\[ E = 3.9756 \times 10^{-19} \, \text{J} \]
Nā, tatauhia te maha o ngā photon i tukuna i te wā \( 1 \, \text{s} \):
Mana \( P = 1 \, \text{W} \):
\[ E_{\text{tapeke}} = P \cdot t = 1 \, \text{W} \times 1 \, \text{s} = 1 \, \text{J} \]
Te maha o ngā photon:
\[ n = \frac{E_{\text{total}}}{E_{\text{photons}}} = \frac{1 \, \text{J}}{3.9756 \times 10^{-19} \, \text{J}} \]
\[ n \tata ki te 2.52 \whakareatia ki te 10^{18} \]
Nō reira, ka tukuna e te taiaho he tata ki te \( 2.52 \times 10^{18} \) ngā photon i roto i te hēkona kotahi.
Whakamutunga
He mea nui te mārama ki te pūngao ngaru hikohiko ki ngā tono maha i roto i ngā momo mara o te hangarau me te pūtaiao. Mā roto i ngā tauira i kōrerohia, kua kite tātou i ngā mahi e uru ana ki te tatau i te pūngao photon i runga i te auau me te roangaru, te huri i waenga i ngā waeine pūngao, me te tatau i te mana hihi. Mā te mahi me te mārama hohonu ake, ka nui haere te mārama me te whai hua o ēnei ariā i roto i ngā tono o te ao tūturu.
