Mienzaniso yeMibvunzo Inotsanangura Dzidziso yaPlanck yeQuantum
Dzidziso yeQuantum yaPlanck yaive nguva yakakosha yekuchinja mufizikisi yemazuva ano, ichichinja kunzwisisa kwedu kwemwaranzi yemuviri mutema uye quantum mechanics. Yakaunzwa naMax Planck muna 1900, dzidziso iyi inobatsira kutsanangura zviitiko izvo fizikisi yekare yaisagona kutsanangura. Chinyorwa chino chichaongorora dzidziso yequantum yaPlanck kuburikidza nekukurukura mienzaniso yezvinetso, kubva papfungwa huru kusvika pakushandiswa.
Nhoroondo yedzidziso yaPlanck yeQuantum
Tisati takurukura nezvedambudziko remuenzaniso, zvakakosha kunzwisisa nhoroondo yePlanck's Quantum Theory. Mukupera kwezana remakore rechi19, fizikisi yekare yakatarisana nedambudziko guru mukutsanangura huwandu hwemwaranzi yemuviri mutema. Mwaranzi yemuviri mutema imwaranzi yemagetsi inoburitswa nezvinhu patembiricha yakatarwa.
Fizikisi yekare, ichishandisa mutemo weRayleigh-Jeans, yakafanotaura kuti simba remwaranzi raizowedzera zvikuru pahuwandu hwemafrequency akakwira, anozivikanwa se "njodzi ye ultraviolet." Apa ndipo pakauya Max Planck nemhinduro itsva: akataura kuti simba rinoburitswa kana kunyudzwa mumapaketi akasiyana anonzi "quanta."
Fomura Yekutanga yeDzidziso yaPlanck yeQuantum
Nzira huru yesimba re quantum maererano nedzidziso yaPlanck ndeiyi:
\[ E = h \nu \]
dimana:
– \( E \) isimba repaketi ye quantum (inonziwo quanta),
– \( h \) ishoko raPlanck risingaperi (\(6.626 \times 10^{-34} \, \text{Js}\)),
– \( \nu \) ndiyo frequency yemwaranzi.
Mibvunzo yemuenzaniso nekukurukurirana
Mubvunzo 1: Kuverenga Simba reQuantum
Mubvunzo:
Photon ine frequency ye \( 5 \times 10^{14} \, \text{Hz} \). Verenga simba rephoton zvichienderana nedzidziso yaPlanck.
Kukurukurirana:
Zvinozivikanwa:
– Kuwanda \( \nu = 5 \kawa 10^{14} \, \text{Hz} \)
– Chinogaroitika chaPlanck \( h = 6.626 \kawa 10^{-34} \, \text{Js} \)
Kushandisa fomura yesimba rePlanck requantum:
\[ E = h \nu \]
\[ E = (6.626 \kawa 10^{-34} \, \text{Js}) \kawa (5 \kawa 10^{14} \, \text{Hz}) \]
\[ E = 3.313 \kawa 10^{-19} \, \mashoko{J} \]
Saka, simba re photon ndiro \( 3.313 \times 10^{-19} \, \text{J} \).
Mubvunzo 2: Hukama Huripo Pakati Pehurefu Hwemafungu Nesimba
Mubvunzo:
Sarudza simba re photon rine urefu hwemafungu e \( 600 \, \text{nm} \).
Kukurukurirana:
Zvinozivikanwa:
– Hurefu hwemafungu \( \lambda = 600 \, \text{nm} = 600 \times 10^{-9} \, \text{m} \)
– Kumhanya kwechiedza \( c = 3 \kawa 10^{8} \, \text{m/s} \)
– Chinogaroitika chaPlanck \( h = 6.626 \kawa 10^{-34} \, \text{Js} \)
Kutanga, tinofanira kuwana frequency \( \nu \) tichishandisa hukama huripo pakati pe wavelength ne frequency:
\[ \nu = \frac{c}{\lambda} \]
\[ \nu = \frac{3 \times 10^{8} \, \text{m/s}}{600 \times 10^{-9} \, \text{m}} \]
\[ \nu = 5 \kawa 10^{14} \, \text{Hz} \]
Iye zvino, tinogona kushandisa fomura yaPlanck yesimba re quantum:
\[ E = h \nu \]
\[ E = (6.626 \kawa 10^{-34} \, \text{Js}) \kawa (5 \kawa 10^{14} \, \text{Hz}) \]
\[ E = 3.313 \kawa 10^{-19} \, \mashoko{J} \]
Saka, simba re photon rine wavelength \( 600 \, \text{nm} \) ndiro \( 3.313 \times 10^{-19} \, \text{J} \).
Mubvunzo 3: Simba Rine Chekuita Nemwaranzi Yemuviri Mutema
Mubvunzo:
Muviri mutema uri patembiricha ye3000 K. Ndeipi frequency yepamusoro yemwaranzi inogadzirwa nechinhu chacho?
Kukurukurirana:
Zvinozivikanwa:
– Tembiricha \( T = 3000 \, \text{K} \)
– Boltzmann's constant \( k = 1.38 \times 10^{-23} \, \text{J/K} \)
Zvinoenderana nemutemo waWien, kureba kwemwaranzi yemuviri mutema \( \lambda_{\text{max}} \) kunoratidzwa ne:
\[ \lambda_{\text{max}} T = 2.898 \kawa 10^{-3} \, \text{m K} \]
Kuti:
\[ \lambda_{\text{max}} = \frac{2.898 \times 10^{-3} \, \text{m K}}{3000 \, \text{K}} \]
\[ \lambda_{\text{max}} = 9.66 \kawa 10^{-7} \, \text{m} \]
Kuti tiwane peak frequency \( \nu_{\text{max}} \), tinoshandisa:
\[ \nu_{\text{max}} = \frac{c}{\lambda_{\text{max}}} \]
\[ \nu_{\text{max}} = \frac{3 \times 10^{8} \, \text{m/s}}{9.66 \times 10^{-7} \, \text{m}} \]
\[ \nu_{\text{max}} \inenge 3.10 \kawa 10^{14} \, \text{Hz} \]
Saka, huwandu hwemwaranzi inogadzirwa nemuviri mutema patembiricha ye3000 K hunenge \( 3.10 \times 10^{14} \, \text{Hz} \).
Mubvunzo 4: Kupararira kweSimba reMwaranzi
Mubvunzo:
Verenga simba rose rinobuda nechiedza chinobuda mumuviri mutema pachikamu chimwe nechimwe chenzvimbo patembiricha ye5000 K.
Kukurukurirana:
Zvinozivikanwa:
– Tembiricha \( T = 5000 \, \text{K} \)
– Stefan-Boltzmann nguva dzose \( \sigma = 5.67 \times 10^{-8} \, \text{W/m}^2\text{K}^4 \)
Nzira yekugoverwa kwesimba rose remwaranzi rinoburitswa nemuviri mutema ndeiyi:
\[ E = \sigma T^4 \]
\[ E = (5.67 \kawa 10^{-8} \, \text{W/m}^2\text{K}^4) \times (5000 \, \text{K})^4 \]
\[ E = 5.67 \kawa 10^{-8} \kawa 625 \kawa 10^{12} \]
\[ E \inenge 3.54375 \kawa 10^{7} \, \text{W/m}^2 \]
Saka, simba rose rinobuda nemuviri mutema patembiricha ye5000 K i \( 3.54375 \times 10^{7} \, \text{W/m}^2 \).
Mhedziso
Dzidziso yeQuantum yaPlanck inopa hwaro hwakakosha hwefizikisi yemazuva ano, kunzwisisa kuti simba rinoburitswa sei uye rinonyudzwa sei muchimiro chequanta. Tichishandisa fomura yekutanga \( E = h \nu \), tinogona kuverenga ruzivo rwakakosha rwakasiyana-siyana, kusanganisira simba rephoton, frequency uye wavelength zvine chekuita nemwaranzi yemagetsi, uye kugoverwa kwesimba remwaranzi kubva mumuviri mutema. Chidzidzo ichi hachina kungoputsa miganhu yefizikisi yekare chete asiwo chakagadzira nzira yekuvandudzwa kwequantum mechanics uye hunyanzvi hwakasiyana-siyana hwetekinoroji.
