Tusaalaha Su'aalaha Doodda Saamaynta Compton
Saamaynta Compton waa dhacdo muhiim ah oo ku jirta fiisigiska kuantumka. Daahfurkani ma aha oo kaliya inuu sii qoto dheereeyo fahamkeenna ku saabsan laba-geesoodka hirarka-qaybta iftiinka laakiin sidoo kale wuxuu bixiyaa caddayn xooggan oo ku saabsan aragtida kuantumka ee shucaaca. Maqaalkani wuxuu dib u eegi doonaa saamaynta Compton, mabaadi'da aasaasiga ah, wuxuuna bixin doonaa tusaalooyin dhibaatooyin iyo xalal ah si loo dabaqo fikraddan.
Fahmidda Saamaynta Compton
Saamaynta Compton, oo loogu magac daray ninkii daahfuray Arthur H. Compton, waa dhacdo uu foton (qayb ka mid ah iftiinka) la kulmo elektaroono oo uu la kulmo isbeddel ku yimaada hirarka. Ka dib marka uu shilku dhaco, foton-ku wuxuu qaar ka mid ah tamartiisa u wareejiyaa elektaroonada, taasoo keenta in photon-ku uu la kulmo koror ku yimaada hirarka (ama hoos u dhaca soo noqnoqoshada).
Isbeddelkan ku yimid hirarka dhererka waxaa loo yaqaan isbeddelka Compton, waxaana lagu muujin karaa isla'egta:
\[
\Delta \lambda = \lambda' – \lambda = \frac{h}{m_ec}(1 – \cos \theta)
\]
diima:
– \(\Delta \lambda\) waa isbeddelka mowjadda hirarka ee fotonka,
– \(\lambda\) waa hirarka bilowga ah ee sawirkan,
– \(\lambda'\) waa hirarka sawirka ka dib shilka,
– \(h\) waa joogtada Planck (\(6.626 \times 10^{-34} \, \text{Js}\)),
– \(m_e\) waa cufka elektaroonka (\(9.109 \times 10^{-31} \, \text{kg}\)),
– \(c\) waa xawaaraha iftiinka (\(3 \times 10^8 \, \text{m/s}\)),
– \(\theta\) waa xagasha kala firdhinta sawirka.
Su'aalo iyo Doodo Tusaale ah
Su'aal 1aad
Fotoon leh hirar dhererkoodu yahay 0,1 nm ayaa ku dhacaya elektaroonik taagan. Fotoonku wuxuu ku kala firirsan yahay xagal 90° ah jihada uu markii hore ka taagnaa. Xisaabi hirarka footoonka ka dib isku dhaca!
Dood:
Waa la ogyahay:
– Hirarka bilowga ah, \(\lambda = 0.1 \, \text{nm} = 0.1 \times 10^{-9} \, \text{m}\)
– Xagasha kala firdhisan, \(\theta = 90^\circle \)
Iyadoo la adeegsanayo isle'egta isbeddelka Compton:
\[
\Delta \lambda = \frac{h}{m_ec}(1 – \cos \theta)
\]
Beddel qiimaha joogtada ah ee Planck, cufka elektarooniga, iyo xawaaraha iftiinka:
\[
\Delta \lambda = \frac{6.626 \jeer 10^{-34}}{9.109 \jeer 10^{-31} \jeer 3 \jeer 10^8}(1 – \cos 90^\circle)
\]
Maadaama \(\cos 90^\circle = 0\),
\[
\Delta \lambda = \frac{6.626 \jeer 10^{-34}}{9.109 \jeer 10^{-31} \jeer 3 \jeer 10^8}
\]
\[
\Delta \lambda = \frac{6.626 \jeer 10^{-34}}{2.7327 \jeer 10^{-22}}
\]
\[
\Delta \lambda = 2.43 \jeer 10^{-12} \, \text{m} = 0.00243 \, \text{nm}
\]
Markaa hirarka ka dib shilku waa:
\[
\lambda' = \lambda + \Delta \lambda = 0.1 \, \text{nm} + 0.00243 \, \text{nm} = 0.10243 \, \text{nm}
\]
Su'aal 2aad
Fotoon leh hirarka \( \lambda = 0.05 \, \text{nm} \) ayaa ku kala firirsan xagal \( \theta = 120^\circ \). Go'aami hirarka fotoonka ka dib kala firdhinta.
Dood:
Waa la ogyahay:
– Hirarka bilowga ah, \(\lambda = 0.05 \, \text{nm} = 0.05 \times 10^{-9} \, \text{m}\)
– Xagasha kala firdhisan, \(\theta = 120^\circle \)
Iyadoo la adeegsanayo isle'egta isbeddelka Compton:
\[
\Delta \lambda = \frac{h}{m_ec}(1 – \cos \theta)
\]
Beddel qiimaha joogtada ah ee Planck, cufka elektarooniga, iyo xawaaraha iftiinka:
\[
\Delta \lambda = \frac{6.626 \jeer 10^{-34}}{9.109 \jeer 10^{-31} \jeer 3 \jeer 10^8}(1 – \cos 120^\circle)
\]
Tan iyo \(\cos 120^\circle = -0.5\),
\[
\Delta \lambda = \frac{6.626 \jeer 10^{-34}}{9.109 \jeer 10^{-31} \jeer 3 \jeer 10^8}(1 – (-0.5))
\]
\[
\Delta \lambda = \frac{6.626 \jeer 10^{-34}}{9.109 \jeer 10^{-31} \jeer 3 \jeer 10^8}(1 + 0.5)
\]
\[
\Delta \lambda = \frac{6.626 \jeer 10^{-34}}{2.7327 \jeer 10^{-22}} \jeer 1.5
\]
\[
\Delta \lambda = 2.43 \jeer 10^{-12} \, \text{m} \jeer 1.5 = 3.645 \jeer 10^{-12} \, \text{m} = 0.003645 \, \text{nm}
\]
Markaa hirarka ka dib shilku waa:
\[
\lambda' = \lambda + \Delta \lambda = 0.05 \, \text{nm} + 0.003645 \, \text{nm} = 0.053645 \, \text{nm}
\]
Su'aal 3aad
Haddii hirarka sawirka ka dib uu yahay 0.045 nm oo xagasha kala firdhintu ay tahay \(60^\circ\), go'aami dhererka sawirka ka hor inta uusan kala firdhisan.
Dood:
Waa la ogyahay:
– Dhererka hirarka ka dib isku dhaca, \(\lambda' = 0.045 \, \text{nm} = 0.045 \times 10^{-9} \, \text{m}\)
– Xagasha kala firdhisan, \(\theta = 60^\circle \)
Iyadoo la adeegsanayo isle'egta isbeddelka Compton:
\[
\Delta \lambda = \frac{h}{m_ec}(1 – \cos \theta)
\]
Beddel qiimaha joogtada ah ee Planck, cufka elektarooniga, iyo xawaaraha iftiinka:
\[
\Delta \lambda = \frac{6.626 \jeer 10^{-34}}{9.109 \jeer 10^{-31} \jeer 3 \jeer 10^8}(1 – \cos 60^\circle)
\]
Maadaama \(\cos 60^\circle = 0.5\),
\[
\Delta \lambda = \frac{6.626 \jeer 10^{-34}}{9.109 \jeer 10^{-31} \jeer 3 \jeer 10^8}(1 - 0.5)
\]
\[
\Delta \lambda = \frac{6.626 \jeer 10^{-34}}{2.7327 \jeer 10^{-22}} \jeer 0.5
\]
\[
\Delta \lambda = 2.43 \jeer 10^{-12} \, \text{m} \jeer 0.5 = 1.215 \jeer 10^{-12} \, \text{m} = 0.001215 \, \text{nm}
\]
Mowjadaha hirarka ka dib shilka waa la yaqaan:
\[
\lambda' = \lambda + \Delta \lambda
\]
Markaa hirarka ka hor inta aan la kala firdhin waa:
\[
\lambda = \lambda' – \Delta \lambda = 0.045 \, \text{nm} – 0.001215 \, \text{nm} = 0.043785 \, \text{nm}
\]
Gabagabo
Fahmidda saameynta Compton waxay noo ogolaanaysaa inaan si fiican u fahanno isdhexgalka u dhexeeya fotonnada iyo elektaroonada macnaha guud ee fiisigiska kuantumka. Isbeddelkan hirarka ee ay sababto kala firdhinta ayaa muujinaya laba-geesoodka hirarka-qaybta iftiinka wuxuuna xoojiyaa aragtida kuantumka ee shucaaca. Tusaalooyinka kor ku xusan waa codsiyada tooska ah ee isle'egta Compton, taas oo naga caawin karta inaan fahanno fikradda aasaasiga ah iyo inaan xisaabino isbeddellada hirarka ee xaaladaha kala duwan.
