Mienzaniso yeMibvunzo Inokurukura Pfungwa yePhotons
Maphotoni zvimedu zvepakutanga zvinoumba hwaro hwedzidziso ye quantum yechiedza. Se quantum yechiedza, photon inotakura simba rine chekuita ne frequency yaro. Pfungwa iyi yakatanga kuunzwa naAlbert Einstein muna 1905. Muchinyorwa chino, tichakurukura mienzaniso yakati wandei nehurukuro pamusoro pemaphotoni kuti tijekese kunzwisisa kwedu nyaya iyi.
Kunzwisisa Kwekutanga kwePhotons
Maphoton zvimedu zvakapfava, kana kuti quanta, zvemwaranzi yemagetsi. Mudzidziso yequantum, maphoton haana zororo asi ane simba uye simba. Simba rephoton rinogona kuverengerwa uchishandisa equation yakagadzirwa naMax Planck:
\[ E = hf \]
Dimana:
– \( E \) isimba re photon
– \( h \) ndiyo nguva dzose yaPlanck ( \( 6.626 \times 10^{-34} \) Js)
– \( f \) ndiyo nguva yechiedza
Hukama huripo pakati pesimba re photon uye wavelength \(\lambda\) hunogona kuratidzwa ne equation inotevera:
\[ E = \frac{hc}{\lambda} \]
Dimana:
– \( c \) ndiko kumhanya kwechiedza mu vacuum \( (3 \kawa 10^8 \) m/s)
Mibvunzo yemuenzaniso nekukurukurirana
Mubvunzo 1: Kuverenga Simba rePhoton
Mubvunzo: Photon ine urefu hwemafungu e500 nm. Verenga simba rephoton mumajoules.
Kukurukurirana:
Kutanga, tinoshandura urefu hwewavelength kubva pa nanometers kuita mamita.
\[ 500 \ \text{nm} = 500 \times 10^{-9} \ \text{m} \]
Kushandisa equation yesimba re photon:
\[ E = \frac{hc}{\lambda} \]
Isa kukosha kwe "constant" yaPlanck ( \( h = 6.626 \times 10^{-34} \) Js) uye kumhanya kwechiedza \( c = 3 \times 10^8 \ \text{m/s} \):
\[ E = \frac{(6.626 \nguva 10^{-34} \ \text{Js}) \nguva (3 \nguva 10^8 \ \text{m/s})}{500 \nguva 10^{-9} \ \text{m}} \]
\[ E = \frac{1.9878 \times 10^{-25}}{500 \times 10^{-9}} \]
\[ E = 3.976 \kawa 10^{-19} \ \mashoko{J} \]
Saka, simba re photon i \( 3.976 \times 10^{-19} \) joules.
Mubvunzo 2: Kuverenga Kuwanda kweSimba rePhoton
Mubvunzo: Kana photon iine simba re \( 2.5 \times 10^{-19} \) joules, frequency yechiedza iyo photon ine chii?
Kukurukurirana:
Tinoshandisa equation yekutanga yesimba re photon:
\[ E = hf \]
Tinoparadzanisa frequency \( f \):
\[ f = \frac{E}{h} \]
Isa kukosha kwesimba \( E \) uye kusachinja kwaPlanck \( h \):
\[ f = \frac{2.5 \times 10^{-19} \ \text{J}}{6.626 \times 10^{-34} \ \text{Js}} \]
\[ f = 3.77 \kawa 10^{14} \ \mashoko{Hz} \]
Saka, frequency yechiedza ndeye \( 3.77 \times 10^{14} \ \text{Hz} \).
Mubvunzo 3: Mhedzisiro yePhotoelectric
Mubvunzo: Mukuyedza kwe photoelectric effect, photon ine simba 4.0 eV inorova pamusoro pesimbi yoburitsa electron. Kana basa resimbi riri 2.5 eV, verenga simba guru re kinetic re electron inoburitswa.
Kukurukurirana:
Simba re photon \( E \) rinopihwa muma electronvolts (eV). Tinogona kushandisa kukosha uku zvakananga nekuti basa rekushanda ririwo mu eV.
Basa rekushanda (\( W \)) ndiro simba shoma rinodiwa kubvisa erekitironi pamusoro pesimbi. Simba guru rekinetic (\( KE \)) reerekitironi rinoverengerwa semusiyano uripo pakati pesimba rephoton nebasa rekushanda:
\[ KE = E – W \]
Isa kukosha kwesimba re photon \( E = 4.0 \\text{eV} \) uye basa rekushanda \( W = 2.5 \\text{eV} \):
\[ KE = 4.0 \ \chinyorwa{eV} – 2.5 \ \chinyorwa{eV} \]
\[ KE = 1.5 \ \mashoko{eV} \]
Saka, simba guru re kinetic remaerekitironi akaburitswa i1.5 eV.
Mubvunzo 4: Kureba kweMafungu Kubva paMafambiro
Mubvunzo: Ndeipi wavelength ye photon ine frequency ye \( 6 \times 10^{14} \ \text{Hz} \)?
Kukurukurirana:
Kushandisa hukama huripo pakati pekumhanya kwechiedza, mafrequency, uye urefu hwewavelength:
\[ c = \lambda f \]
Tinoparadzanisa urefu hwewavelength \( \lambda \):
\[ \lambda = \frac{c}{f} \]
Isa mavalues ekukurumidza kwechiedza \( c = 3 \times 10^8 \ \text{m/s} \) uye frequency \( f = 6 \times 10^{14} \ \text{Hz} \):
\[ \lambda = \frac{3 \times 10^8 \ \text{m/s}}{6 \times 10^{14} \ \text{Hz}} \]
\[ \lambda = 5 \kawa 10^{-7} \ \text{m} \]
\[ \lambda = 500 \ \text{nm} \]
Saka, urefu hwemafungu e photon i500 nm.
Mubvunzo 5: Simba rePhoton muSpectrum
Mubvunzo: Photon iri mu ultraviolet spectrum ine wavelength ye 150 nm. Verenga simba re photon muma joules nema electronvolts.
Kukurukurirana:
Kutanga, shandura urefu hwemafungu kuita mamita:
\[ 150 \ \text{nm} = 150 \times 10^{-9} \ \text{m} \]
Kuverenga simba re photon mu joules:
\[ E = \frac{hc}{\lambda} \]
Isa kukosha:
\[ E = \frac{(6.626 \nguva 10^{-34} \ \text{Js}) \nguva (3 \nguva 10^8 \ \text{m/s})}{150 \nguva 10^{-9} \ \text{m}} \]
\[ E = \frac{1.9878 \times 10^{-25}}{150 \times 10^{-9}} \]
\[ E = 1.3252 \kawa 10^{-18} \ \mashoko{J} \]
Kuti tishandure majoules kuita ma electronvolts, tinoshandisa 1eV = \( 1.602 \times 10^{-19} \) J:
\[ E \ (\text{eV}) = \frac{1.3252 \times 10^{-18} \ \text{J}}{1.602 \times 10^{-19} \ \text{J/eV}} \]
\[ E \ (\ zvinyorwa{eV}) = 8.27 \ \ zvinyorwa{eV} \]
Saka, simba re ultraviolet photon i \( 1.3252 \times 10^{-18} \ \text{J} \) kana 8.27 eV.
Mhedziso
Kubva mumatambudziko akasiyana-siyana emuenzaniso nehurukuro dziri pamusoro apa, tanyatsoongorora hunhu nekuverenga zvine chekuita nemaphoton. Izvi zvinosanganisira kuverenga simba zvichibva pahurefu hwewavelength uye frequency, pamwe nekushandiswa kwepfungwa yephoton mumhedzisiro yephoton. Kunzwisisa pfungwa yephoton kwakakosha kwete chete mufizikisi yedzidziso asiwo mumashandisirwo akasiyana-siyana etekinoroji yemazuva ano akadai sephotovoltaics, lasers, uye light sensors. Nekudzidzira kwakakwana, kunzwisisa pfungwa idzi kuchava nyore uye kunzwisisika.
