Mehlala ea Lipotso tse Buisanang ka Khopolo-taba ea Planck ea Quantum
Khopolo-taba ea Planck ea Quantum e bile ntlha ea bohlokoa ea phetoho fisiks ea sejoale-joale, e fetola kutloisiso ea rona ea mahlaseli a 'mele o motšo le mechanics ea quantum. E hlahisitsoe ke Max Planck ka 1900, khopolo-taba ena e thusa ho hlalosa liketsahalo tseo fisiks ea khale e neng e ke ke ea li hlalosa. Sengoloa sena se tla hlahloba khopolo-taba ea Planck ea quantum ka puisano ea mehlala ea mathata, ho tloha likhopolong tsa motheo ho ea lits'ebetsong.
Semelo sa Khopolo-taba ea Quantum ea Planck
Pele ho tšohloa bothata ba mohlala, ho bohlokoa ho utloisisa nalane ea Khopolo-taba ea Planck ea Quantum. Mafelong a lekholo la bo19 la lilemo, fisiks ea khale e ile ea tobana le phephetso e kholo ho hlaloseng mefuta e fapaneng ea mahlaseli a 'mele o motšo. Mahlaseli a 'mele o motšo ke mahlaseli a motlakase a ntšoang ke lintho mochesong o itseng.
Fisiks ea khale, e sebelisa molao oa Rayleigh-Jeans, e ile ea bolela esale pele hore matla a mahlaseli a tla eketseha ka mokhoa o sa feleng maqhubung a phahameng, a tsejoang e le "koluoa ea ultraviolet." Mona ke moo Max Planck a ileng a tla ka tharollo e ncha: o ile a sisinya hore matla a ntšoe kapa a monyeloe ka har'a lipakete tse arohaneng tse bitsoang "quanta."
Foromo ea Motheo ea Khopolo-taba ea Planck ea Quantum
Foromo ea motheo ea matla a quantum ho latela khopolo-taba ea Planck ke:
\[ E = h \nu \]
Moo:
– \( E \) ke matla a pakete ea quantum (eo hape e bitsoang quanta),
– \( h \) ke phetolelo ya kamehla ya Planck (\(6.626 \times 10^{-34} \, \text{Js}\)),
– \( \nu \) ke maqhubu a mahlaseli.
Lipotso tsa Mehlala le Puisano
Potso ea 1: Palo ea Matla a Quantum
Potso:
Foton e na le maqhubu a \( 5 \makgetlo a 10^{14} \, \text{Hz} \). Bala matla a photon ho latela khopolo-taba ea Planck.
Puisano:
Hoa tsebahala:
– Makgetlo \( \nu = 5 \makgetlo a 10^{14} \, \text{Hz} \)
– Phetoho ya Planck \( h = 6.626 \makgetlo a 10^{-34} \, \text{Js} \)
Ho sebelisa foromo ea Planck ea matla a quantum:
\[ E = h \nu \]
\[ E = (6.626 \makgetlo a 10^{-34} \, \mongolo{Js}) \makgetlo (5 \makgetlo a 10^{14} \, \mongolo{Hz}) \]
\[ E = 3.313 \makgetlo a 10^{-19} \, \mongolo{J} \]
Kahoo, matla a photon ke \( 3.313 \times 10^{-19} \, \text{J} \).
Potso ea 2: Kamano Pakeng tsa Bolelele ba Maqhubu le Matla
Potso:
Fumana matla a photon e nang le bolelele ba leqhubu ba \( 600 \, \text{nm} \).
Puisano:
Hoa tsebahala:
– Bolelele ba maqhubu \( \lambda = 600 \, \text{nm} = 600 \times 10^{-9} \, \text{m} \)
– Lebelo la leseli \( c = 3 \makgetlo a 10^{8} \, \text{m/s} \)
– Phetoho ya Planck \( h = 6.626 \makgetlo a 10^{-34} \, \text{Js} \)
Taba ea pele, re hloka ho fumana maqhubu \( \nu \) re sebelisa kamano pakeng tsa bolelele ba wavelength le maqhubu:
\[ \nu = \frac{c}{\lambda} \]
\[ \nu = \frac{3 \times 10^{8} \, \text{m/s}}{600 \times 10^{-9} \, \text{m}} \]
\[ \nu = 5 \makgetlo a 10^{14} \, \mongolo{Hz} \]
Jwale, re ka sebedisa foromo ya Planck ya matla a quantum:
\[ E = h \nu \]
\[ E = (6.626 \makgetlo a 10^{-34} \, \mongolo{Js}) \makgetlo (5 \makgetlo a 10^{14} \, \mongolo{Hz}) \]
\[ E = 3.313 \makgetlo a 10^{-19} \, \mongolo{J} \]
Kahoo, matla a photon a nang le bolelele ba wavelength \( 600 \, \text{nm} \) ke \( 3.313 \times 10^{-19} \, \text{J} \).
Potso ea 3: Matla a Amanang le Mahlaseli a 'Mele o Motšo
Potso:
'Mele o motsho o mochesong oa 3000 K. Maqhubu a phahameng a mahlaseli a hlahisoang ke ntho ke afe?
Puisano:
Hoa tsebahala:
– Mocheso \( T = 3000 \, \mongolo{K} \)
– Boltzmann's kamehla \( k = 1.38 \times 10^{-23} \, \text{J/K} \)
Ho ya ka molao wa Wien, bolelele ba leqhubu la maqhubu a tlhōrō \( \lambda_{\text{max}} \) ba mahlaseli a mmele o motsho bo fanwa ke:
\[ \lambda_{\text{max}} T = 2.898 \makgetlo a 10^{-3} \, \text{m K} \]
E le hore:
\[ \lambda_{\text{max}} = \frac{2.898 \times 10^{-3} \, \text{m K}}{3000 \, \text{K}} \]
\[ \lambda_{\text{max}} = 9.66 \makgetlo a 10^{-7} \, \text{m} \]
Ho fumana maqhubu a tlhoro \( \nu_{\text{max}} \), re sebedisa:
\[ \nu_{\text{max}} = \frac{c}{\lambda_{\text{max}}} \]
\[ \nu_{\text{max}} = \frac{3 \times 10^{8} \, \text{m/s}}{9.66 \times 10^{-7} \, \text{m}} \]
\[ \nu_{\text{max}} \hoo e ka bang 3.10 \makgetlo a 10^{14} \, \text{Hz} \]
Kahoo, maqhubu a phahameng a mahlaseli a hlahisoang ke 'mele o motšo mochesong oa 3000 K a ka ba \( 3.10 \makhetlo a 10^{14} \, \text{Hz} \).
Potso ea 4: Kabo ea Matla a Mahlaseli
Potso:
Bala kakaretso ea matla a mahlaseli a tsoang 'meleng o motšo ka sebaka sa bokaholimo ba yuniti mochesong oa 5000 K.
Puisano:
Hoa tsebahala:
– Mocheso \( T = 5000 \, \mongolo{K} \)
– Stefan-Boltzmann kamehla \( \sigma = 5.67 \times 10^{-8} \, \text{W/m}^2\text{K}^4 \)
Foromo ea kabo ea matla a mahlaseli 'ohle a hlahisoang ke 'mele o motšo ke:
\[ E = \sigma T^4 \]
\[ E = (5.67 \ka makhetlo a 10^{-8} \, \mongolo{W/m}^2\mongolo{K}^4) \ka makhetlo (5000 \, \mongolo{K})^4 \]
\[ E = 5.67 \makgetlo a 10^{-8} \makgetlo a 625 \makgetlo a 10^{12} \]
\[ E \hoo e ka bang 3.54375 \makgetlo a 10^{7} \, \mongolo{W/m}^2 \]
Kahoo, matla ohle a mahlaseli a ntšoang ke 'mele o motšo mochesong oa 5000 K ke \( 3.54375 \times 10^{7} \, \text{W/m}^2 \).
Qetello
Khopolo-taba ea Planck ea Quantum e fana ka motheo oa bohlokoa bakeng sa fisiks ea sejoale-joale, ho utloisisa hore na matla a ntšoa le ho monngoa joang ka mokhoa oa quanta. Re sebelisa foromo ea motheo \( E = h \nu \), re ka bala tlhaiso-leseling e fapaneng ea bohlokoa, ho kenyeletsoa matla a photon, maqhubu le bolelele ba leqhubu bo amanang le mahlaseli a motlakase, le kabo ea matla a mahlaseli a tsoang 'meleng o motšo. Phuputso ena ha ea ka ea roba meeli ea fisiks ea khale feela empa hape e buletse tsela bakeng sa nts'etsopele ea mechini ea quantum le boqapi bo fapaneng ba theknoloji.
