Mehlala ea Lipotso tse Buisanang ka Phello ea Compton
Phello ea Compton ke ketsahalo ea bohlokoa fisiks ea quantum. Tšibollo ena ha e tebise kutloisiso ea rona feela ea bobeli ba maqhubu le likaroloana tsa leseli empa hape e fana ka bopaki bo matla ba khopolo-taba ea quantum ea mahlaseli. Sengoloa sena se tla hlahloba phello ea Compton, melao-motheo ea eona ea motheo, le ho fana ka mehlala ea mathata le litharollo tsa ho sebelisa mohopolo ona.
Ho utloisisa phello ea Compton
Phello ea Compton, e reheletsoeng ka mosireletsi oa eona Arthur H. Compton, ke ketsahalo eo ho eona photon (karoloana ea leseli) e thulanang le elektrone 'me e ba le phetoho ea bolelele ba leqhubu. Kamora ho thulana, photon e fetisetsa matla a mang a eona ho elektrone, e leng se etsang hore photon e be le keketseho ea bolelele ba leqhubu (kapa phokotso ea maqhubu).
Phetoho ena ea bolelele ba leqhubu e bitsoa phetoho ea Compton, 'me e ka hlalosoa ke equation:
\[
\Delta \lambda = \lambda' – \lambda = \frac{h}{m_ec}(1 – \cos \theta)
\]
Moo:
– \(\Delta \lambda\) ke phetoho ya bolelele ba leqhubu la photon,
– \(\lambda\) ke bolelele ba leqhubu la pele la photon,
– \(\lambda'\) ke bolelele ba leqhubu la photon ka mora ho thulana,
– \(h\) ke phetolelo ya Planck e sa fetoheng (\(6.626 \times 10^{-34} \, \text{Js}\)),
– \(m_e\) ke boima ba elektrone (\(9.109 \times 10^{-31} \, \text{kg}\)),
– \(c\) ke lebelo la lesedi (\(3 \makgetlo a 10^8 \, \text{m/s}\)),
– \(\theta\) ke sekhutlo sa ho hasana ha photon.
Lipotso tsa Mehlala le Puisano
Potso ea 1
Foton e nang le bolelele ba leqhubu ba 0,1 nm e otla elektrone e sa sisinyeheng. Foton e ntan'o hasana ka sekhutlo sa 90° ho tloha lehlakoreng la eona la pele. Bala bolelele ba leqhubu la photon ka mor'a ho thulana!
Puisano:
Hoa tsebahala:
– Bolelele ba maqhubu a qalong, \(\lambda = 0.1 \, \text{nm} = 0.1 \times 10^{-9} \, \text{m}\)
– Sekhutlo se hasanyang, \(\theta = 90^\circ \)
Ho sebelisa equation ea phetoho ea Compton:
\[
\Delta \lambda = \frac{h}{m_ec}(1 – \cos \theta)
\]
Kenya boleng ba ntho e sa fetoheng ea Planck, boima ba elektrone le lebelo la khanya sebakeng sa eona:
\[
\Delta \lambda = \frac{6.626 \times 10^{-34}}{9.109 \times 10^{-31} \times 3 \times 10^8}(1 – \cos 90^\circ)
\]
Kaha \(\cos 90^\circ = 0\),
\[
\Delta \lambda = \frac{6.626 \times 10^{-34}}{9.109 \times 10^{-31} \times 3 \times 10^8}
\]
\[
\Delta \lambda = \frac{6.626 \times 10^{-34}}{2.7327 \times 10^{-22}}
\]
\[
\Delta \lambda = 2.43 \makgetlo a 10^{-12} \, \text{m} = 0.00243 \, \text{nm}
\]
Kahoo bolelele ba leqhubu ka mor'a ho thulana ke:
\[
\lambda' = \lambda + \Delta \lambda = 0.1 \, \text{nm} + 0.00243 \, \text{nm} = 0.10243 \, \text{nm}
\]
Potso ea 2
Foton e nang le bolelele ba leqhubu \( \lambda = 0.05 \, \text{nm} \) e hasane ka sekhutlo \( \theta = 120^\circ \). Fumana bolelele ba leqhubu la photon kamora ho hasana.
Puisano:
Hoa tsebahala:
– Bolelele ba maqhubu a qalong, \(\lambda = 0.05 \, \text{nm} = 0.05 \times 10^{-9} \, \text{m}\)
– Sekhutlo se hasanyang, \(\theta = 120^\circ \)
Ho sebelisa equation ea phetoho ea Compton:
\[
\Delta \lambda = \frac{h}{m_ec}(1 – \cos \theta)
\]
Kenya boleng ba ntho e sa fetoheng ea Planck, boima ba elektrone le lebelo la khanya sebakeng sa eona:
\[
\Delta \lambda = \frac{6.626 \times 10^{-34}}{9.109 \times 10^{-31} \times 3 \times 10^8}(1 – \cos 120^\circ)
\]
Kaha \(\cos 120^\circ = -0.5\),
\[
\Delta \lambda = \frac{6.626 \times 10^{-34}}{9.109 \times 10^{-31} \times 3 \times 10^8}(1 – (-0.5))
\]
\[
\Delta \lambda = \frac{6.626 \times 10^{-34}}{9.109 \times 10^{-31} \times 3 \times 10^8}(1 + 0.5)
\]
\[
\Delta \lambda = \frac{6.626 \times 10^{-34}}{2.7327 \times 10^{-22}} \times 1.5
\]
\[
\Delta \lambda = 2.43 \ka makhetlo a 10^{-12} \, \text{m} \ka makhetlo a 1.5 = 3.645 \ka makhetlo a 10^{-12} \, \text{m} = 0.003645 \, \text{nm}
\]
Kahoo bolelele ba leqhubu ka mor'a ho thulana ke:
\[
\lambda' = \lambda + \Delta \lambda = 0.05 \, \text{nm} + 0.003645 \, \text{nm} = 0.053645 \, \text{nm}
\]
Potso ea 3
Haeba bolelele ba leqhubu la photon ka mora ho hasana e le 0.045 nm mme sekhutlo sa ho hasana e le \(60^\circ\), fumana bolelele ba leqhubu la photon pele o hasana.
Puisano:
Hoa tsebahala:
– Bolelele ba maqhubu ka mora ho thulana, \(\lambda' = 0.045 \, \text{nm} = 0.045 \times 10^{-9} \, \text{m}\)
– Sekhutlo se hasanyang, \(\theta = 60^\circ \)
Ho sebelisa equation ea phetoho ea Compton:
\[
\Delta \lambda = \frac{h}{m_ec}(1 – \cos \theta)
\]
Kenya boleng ba ntho e sa fetoheng ea Planck, boima ba elektrone le lebelo la khanya sebakeng sa eona:
\[
\Delta \lambda = \frac{6.626 \times 10^{-34}}{9.109 \times 10^{-31} \times 3 \times 10^8}(1 – \cos 60^\circ)
\]
Kaha \(\cos 60^\circ = 0.5\),
\[
\Delta \lambda = \frac{6.626 \times 10^{-34}}{9.109 \times 10^{-31} \times 3 \times 10^8}(1 – 0.5)
\]
\[
\Delta \lambda = \frac{6.626 \times 10^{-34}}{2.7327 \times 10^{-22}} \times 0.5
\]
\[
\Delta \lambda = 2.43 \ka makhetlo a 10^{-12} \, \text{m} \ka makhetlo a 0.5 = 1.215 \ka makhetlo a 10^{-12} \, \text{m} = 0.001215 \, \text{nm}
\]
Bolelele ba maqhubu ka mor'a ho thulana boa tsebahala:
\[
\lambda' = \lambda + \Delta \lambda
\]
Kahoo bolelele ba leqhubu pele ho hasana ke:
\[
\lambda = \lambda' – \Delta \lambda = 0.045 \, \text{nm} – 0.001215 \, \text{nm} = 0.043785 \, \text{nm}
\]
Qetello
Ho utloisisa phello ea Compton ho re lumella ho utloisisa hamolemo tšebelisano-'moho lipakeng tsa li-photon le lielektrone moelelong oa fisiks ea quantum. Phetoho ena ea bolelele ba leqhubu ka lebaka la ho hasana e bontša bobeli ba leqhubu le likaroloana tsa leseli 'me e matlafatsa khopolo-taba ea quantum ea mahlaseli. Mehlala e kaholimo ke ts'ebeliso e tobileng ea equation ea Compton, e ka re thusang ho utloisisa mohopolo oa motheo le ho bala liphetoho tsa bolelele ba leqhubu tlas'a maemo a fapaneng.
