Cov Lus Nug Piv Txwv Sib Tham Txog Qhov Cuam Tshuam Compton
Qhov Compton effect yog ib qho tseem ceeb hauv quantum physics. Qhov kev tshawb pom no tsis yog tsuas yog ua rau peb nkag siab tob txog qhov sib txawv ntawm lub teeb thiab lub teeb me me xwb tab sis kuj muab pov thawj zoo rau txoj kev xav ntawm quantum radiation. Tsab xov xwm no yuav tshuaj xyuas qhov Compton effect, nws cov ntsiab cai yooj yim, thiab muab qee qhov piv txwv ntawm cov teeb meem thiab kev daws teeb meem los siv lub tswv yim no.
Nkag Siab Txog Qhov Cuam Tshuam Compton
Qhov Compton effect, uas muab lub npe raws li tus neeg tshawb pom Arthur H. Compton, yog ib qho xwm txheej uas photon (ib qho me me ntawm lub teeb) sib tsoo nrog ib lub electron thiab muaj kev hloov pauv ntawm qhov wavelength. Tom qab kev sib tsoo, lub photon hloov qee lub zog mus rau lub electron, ua rau lub photon muaj kev nce ntawm qhov wavelength (lossis txo qis ntawm qhov zaus).
Qhov kev hloov pauv ntawm wavelength no hu ua Compton shift, thiab tuaj yeem qhia los ntawm cov qauv:
\[
\Delta \lambda = \lambda' – \lambda = \frac{h}{m_ec}(1 – \cos \theta)
\]
Qhov twg:
- \(\Delta \lambda\) yog qhov kev hloov pauv ntawm qhov wavelength ntawm photon,
- \(\lambda\) yog qhov pib ntawm qhov wavelength ntawm photon,
- \(\lambda'\) yog qhov wavelength ntawm photon tom qab kev sib tsoo,
- \(h\) yog Planck tus nqi tas mus li (\(6.626 \times 10^{-34} \, \text{Js}\)),
- \(m_e\) yog qhov hnyav ntawm ib lub electron (\(9.109 \times 10^{-31} \, \text{kg}\)),
- \(c\) yog qhov ceev ntawm lub teeb (\(3 \times 10^8 \, \text{m/s}\)),
- \(\theta\) yog lub kaum sab xis ntawm kev tawg ntawm photon.
Cov Lus Nug Piv Txwv thiab Kev Sib Tham
Lo lus nug thib 1
Ib lub photon uas muaj qhov ntev ntawm 0,1 nm ntaus ib lub electron uas nyob ruaj khov. Tom qab ntawd lub photon raug tawg ntawm lub kaum sab xis 90° ntawm nws qhov kev taw qhia thawj. Xam qhov ntev ntawm lub photon tom qab kev sib tsoo!
Kev Sib Tham:
Nws paub tias:
– Qhov pib ntawm qhov ntev ntawm lub teeb, \(\lambda = 0.1 \, \text{nm} = 0.1 \times 10^{-9} \, \text{m}\)
- Lub kaum sab xis tawg, ∑ (\theta = 90^\circ)
Siv cov qauv Compton shift:
\[
\Delta \lambda = \frac{h}{m_ec}(1 – \cos \theta)
\]
Hloov cov nqi ntawm Planck qhov tsis tu ncua, qhov hnyav ntawm electron, thiab qhov ceev ntawm lub teeb:
\[
\Delta \lambda = \frac{6.626 \times 10^{-34}}{9.109 \times 10^{-31} \times 3 \times 10^8}(1 – \cos 90^\circ)
\]
Vim tias \(\cos 90^\circ = 0\),
\[
\Delta \lambda = \frac{6.626 \times 10^{-34}}{9.109 \times 10^{-31} \times 3 \times 10^8}
\]
\[
\Delta \lambda = \frac{6.626 \times 10^{-34}}{2.7327 \times 10^{-22}}
\]
\[
\Delta \lambda = 2.43 \times 10^{-12} \, \text{m} = 0.00243 \, \text{nm}
\]
Yog li ntawd, qhov wavelength tom qab kev sib tsoo yog:
\[
\lambda' = \lambda + \Delta \lambda = 0.1 \, \text{nm} + 0.00243 \, \text{nm} = 0.10243 \, \text{nm}
\]
Lo lus nug thib 2
Ib lub photon uas muaj qhov ntev ntawm lub teeb (\lambda = 0.05), raug tawg ua tej daim me me (\theta = 120^\circ). Txheeb xyuas qhov ntev ntawm lub teeb tom qab kev tawg ua tej daim me me.
Kev Sib Tham:
Nws paub tias:
– Qhov pib ntawm qhov ntev ntawm lub teeb, \(\lambda = 0.05 \, \text{nm} = 0.05 \times 10^{-9} \, \text{m}\)
- Lub kaum sab xis tawg, ∑ (\theta = 120^\circ)
Siv cov qauv Compton shift:
\[
\Delta \lambda = \frac{h}{m_ec}(1 – \cos \theta)
\]
Hloov cov nqi ntawm Planck qhov tsis tu ncua, qhov hnyav ntawm electron, thiab qhov ceev ntawm lub teeb:
\[
\Delta \lambda = \frac{6.626 \times 10^{-34}}{9.109 \times 10^{-31} \times 3 \times 10^8}(1 – \cos 120^\circ)
\]
Txij li thaum \(\cos 120^\circ = -0.5\),
\[
\Delta \lambda = \frac{6.626 \times 10^{-34}}{9.109 \times 10^{-31} \times 3 \times 10^8}(1 – (-0.5))
\]
\[
\Delta \lambda = \frac{6.626 \times 10^{-34}}{9.109 \times 10^{-31} \times 3 \times 10^8}(1 + 0.5)
\]
\[
\Delta \lambda = \frac{6.626 \times 10^{-34}}{2.7327 \times 10^{-22}} \times 1.5
\]
\[
\Delta \lambda = 2.43 \times 10^{-12} \, \text{m} \times 1.5 = 3.645 \times 10^{-12} \, \text{m} = 0.003645 \, \text{nm}
\]
Yog li ntawd, qhov wavelength tom qab kev sib tsoo yog:
\[
\lambda' = \lambda + \Delta \lambda = 0.05 \, \text{nm} + 0.003645 \, \text{nm} = 0.053645 \, \text{nm}
\]
Lo lus nug thib 3
Yog tias qhov wavelength ntawm photon tom qab scattering yog 0.045 nm thiab lub kaum sab xis ntawm scattering yog ∞ (60^∞ circ), txiav txim siab qhov wavelength ntawm photon ua ntej scattering.
Kev Sib Tham:
Nws paub tias:
- Qhov ntev ntawm lub zog tom qab kev sib tsoo, \(\lambda' = 0.045 \, \text{nm} = 0.045 \times 10^{-9} \, \text{m}\)
- Lub kaum sab xis tawg, ∑ (\theta = 60^\circ)
Siv cov qauv Compton shift:
\[
\Delta \lambda = \frac{h}{m_ec}(1 – \cos \theta)
\]
Hloov cov nqi ntawm Planck qhov tsis tu ncua, qhov hnyav ntawm electron, thiab qhov ceev ntawm lub teeb:
\[
\Delta \lambda = \frac{6.626 \times 10^{-34}}{9.109 \times 10^{-31} \times 3 \times 10^8}(1 – \cos 60^\circ)
\]
Vim tias \(\cos 60^\circ = 0.5\),
\[
\Delta \lambda = \frac{6.626 \times 10^{-34}}{9.109 \times 10^{-31} \times 3 \times 10^8}(1 – 0.5)
\]
\[
\Delta \lambda = \frac{6.626 \times 10^{-34}}{2.7327 \times 10^{-22}} \times 0.5
\]
\[
\Delta \lambda = 2.43 \times 10^{-12} \, \text{m} \times 0.5 = 1.215 \times 10^{-12} \, \text{m} = 0.001215 \, \text{nm}
\]
Lub wavelength tom qab kev sib tsoo paub:
\[
\lambda' = \lambda + \Delta \lambda
\]
Yog li ntawd, qhov wavelength ua ntej kev tawg yog:
\[
\lambda = \lambda' – \Delta \lambda = 0.045 \, \text{nm} – 0.001215 \, \text{nm} = 0.043785 \, \text{nm}
\]
Xaus
Kev nkag siab txog qhov Compton effect ua rau peb nkag siab zoo dua txog kev sib cuam tshuam ntawm photons thiab electrons hauv cov ntsiab lus ntawm quantum physics. Qhov kev hloov pauv ntawm qhov wavelength no vim yog qhov tawg ua qhia txog qhov sib txawv ntawm lub teeb thiab ua kom lub zog ntawm quantum theory ntawm kev tawg. Cov piv txwv saum toj no yog kev siv ncaj qha ntawm Compton equation, uas tuaj yeem pab peb nkag siab txog lub tswv yim yooj yim thiab xam qhov kev hloov pauv ntawm qhov wavelength nyob rau hauv ntau yam mob.
