Tambayoyi Misali Game da Ra'ayin Photons
Photons su ne ƙananan ƙwayoyin halitta waɗanda suka zama tushen ka'idar kwantum ta haske. A matsayin kwantum na haske, photon yana ɗauke da fakitin kuzari wanda ke da alaƙa kai tsaye da mitarsa. Albert Einstein ne ya fara gabatar da wannan ra'ayi a cikin 1905. A cikin wannan labarin, za mu tattauna misalai da tattaunawa da dama game da photons don fayyace fahimtarmu game da wannan batu.
Fahimtar Asali Game da Photons
Photons barbashi ne masu haske, ko kuma quanta, na hasken lantarki. A cikin ka'idar quantum, photons ba su da isasshen taro amma suna da kuzari da ƙarfin motsi. Ana iya ƙididdige kuzarin photon ta amfani da lissafin da Max Planck ya ƙirƙira:
\[ E = hf \]
Ina:
– \( E \) shine makamashin photon
– \(h \) shine daidaitaccen Planck ( \( 6.626 \sau 10^{-34} \) Js)
– \( f \) shine mitar haske
Ana iya bayyana alaƙar da ke tsakanin kuzarin photon da tsawon rai \(\lambda\) ta hanyar lissafin da ke ƙasa:
\[ E = \frac{hc}{\lambda} \]
Ina:
– \( c \) shine saurin haske a cikin injin injin \( (sau 3 10^8 \) m/s)
Tambayoyi da Tattaunawa Samfura
Tambaya ta 1: Lissafin Makamashin Photon
Tambaya: Photon yana da tsawon zango na 500 nm. Lissafa kuzarin photon a cikin joules.
Tattaunawa:
Da farko, muna canza tsawon tsayin nanometer daga nanometer zuwa mita.
\[ 500 \ \text{nm} = 500 \sau 10^{-9} \ \text{m} \]
Amfani da lissafin makamashin photon:
\[ E = \frac{hc}{\lambda} \]
Shigar da ƙimar Planck's constant (\( h = 6.626 \times 10^{-34} \) Js) da kuma saurin haske \( c = 3 \times 10^8 \ \text{m/s} \):
\[ E = \frac{(6.626 \sau 10^{-34} \ \text{Js}) \sau (sau 3 10^8 \ \text{m/s})}{500 \sau 10^{-9} \ \text{m}} \]
\[ E = \frac{1.9878 \sau 10^{-25}}{500 \sau 10^{-9}} \]
\[ E = 3.976 \sau 10^{-19} \ \text{J} \]
Don haka, kuzarin photon shine joules (3.976 sau 10^{-19} \).
Tambaya ta 2: Lissafin Mitar Ƙarfin Photon
Tambaya: Idan photon yana da kuzarin joules sau 2.5 10^{-19} \), menene mitar hasken da photon yake da shi?
Tattaunawa:
Muna amfani da daidaitattun asali na makamashin photon:
\[ E = hf \]
Mun ware mitar \( f \):
\[ f = \frac{E}{h} \]
Shigar da ƙimar makamashi \(E \) da kuma madaidaitan Planck \(h \):
\[ f = \frac{2.5 \sau 10^{-19} \ \text{J}}{6.626 \sau 10^{-34} \ \text{Js}} \]
\[ f = 3.77 \sau 10^{14} \ \text{Hz} \]
Don haka, mitar haske shine \( 3.77 \sau 10^{14} \ \text{Hz} \).
Tambaya ta 3: Tasirin Hoto na lantarki
Tambaya: A cikin gwajin tasirin photoelectric, wani photon mai kuzari 4.0 eV yana buga saman ƙarfe kuma yana fitar da electron. Idan aikin ƙarfen shine 2.5 eV, ƙididdige matsakaicin kuzarin motsi na electron da aka saki.
Tattaunawa:
Ana bayar da makamashin photon \( E \) a cikin electronvolts (eV). Za mu iya amfani da wannan ƙimar kai tsaye saboda aikin aikin shima yana cikin eV.
Aikin aiki (\( W \)) shine mafi ƙarancin kuzarin da ake buƙata don cire electron daga saman ƙarfe. Matsakaicin kuzarin motsi (\( KE \)) na electron ana ƙididdige shi azaman bambanci tsakanin kuzarin photon da aikin aiki:
\[ KE = E – W \]
Shigar da ƙimar makamashin photon \( E = 4.0 \\text{eV} \) da aikin aiki \( W = 2.5 \\text{eV} \):
\[ KE = 4.0 \ \ rubutu {eV} - 2.5 \ \ rubutu {eV} \]
\[ KE = 1.5 \ \text{eV} \]
Don haka, matsakaicin kuzarin motsi na electron da aka saki shine 1.5 eV.
Tambaya ta 4: Tsawon Wave Daga Mita
Tambaya: Menene tsawon tsawon photon wanda ke da mitar \( sau 6 10^{14} \ \text{Hz} \)?
Tattaunawa:
Amfani da alaƙar da ke tsakanin saurin haske, mita, da tsawon tsayi:
\[ c = \lambda f \]
Mun ware tsawon tsayin \( \lambda \):
\[ \lambda = \frac{c}{f} \]
Shigar da ƙimar gudun haske \( c = 3 \times 10^8 \ \text{m/s} \) da mita \( f = 6 \times 10^{14} \ \text{Hz} \):
\[ \lambda = \frac{3 \sau 10^8 \ \text{m/s}}{6 \sau 10^{14} \ \text{Hz}} \]
\[ \lambda = 5 \sau 10^{-7} \ \text{m} \]
\[ \lambda = 500 \ \text{nm} \]
Don haka, tsawon ruwan photon shine 500 nm.
Tambaya ta 5: Makamashin Photon a cikin Bakan
Tambaya: Photon a cikin hasken ultraviolet yana da tsawon tsayin nm 150. Lissafa kuzarin photon a cikin joules da electronvolts.
Tattaunawa:
Da farko, canza tsawon tsayi zuwa mita:
\[ 150 \ \text{nm} = 150 \sau 10^{-9} \ \text{m} \]
Lissafin kuzarin photon a cikin joules:
\[ E = \frac{hc}{\lambda} \]
Shigar da dabi'u:
\[ E = \frac{(6.626 \sau 10^{-34} \ \text{Js}) \sau (sau 3 10^8 \ \text{m/s})}{150 \sau 10^{-9} \ \text{m}} \]
\[ E = \frac{1.9878 \sau 10^{-25}}{150 \sau 10^{-9}} \]
\[ E = 1.3252 \sau 10^{-18} \ \text{J} \]
Don canza joules zuwa electronvolts, muna amfani da 1eV = \( 1.602 \times 10^{-19} \) J:
\[ E \ (\text{eV}) = \frac{1.3252 \times 10^{-18} \ \text{J}}{1.602 \times 10^{-19} \ \text{J/eV}} \]
\[ E \ (\rubutu {eV}) = 8.27 \ rubutu {eV} \]
Don haka, kuzarin hasken ultraviolet photon shine (1.3252 sau 10^{-18} \ \text{J} \) ko 8.27 eV.
Kammalawa
Daga misalai daban-daban da tattaunawa da aka yi a sama, mun zurfafa cikin halaye da lissafin da suka shafi photons. Wannan ya haɗa da lissafin kuzari bisa ga tsawon rai da mita, da kuma amfani da ra'ayin photon a cikin tasirin photoelectric. Fahimtar ra'ayin photon yana da mahimmanci ba kawai a cikin kimiyyar lissafi ba har ma a cikin aikace-aikacen fasaha na zamani daban-daban kamar su photovoltaics, lasers, da firikwensin haske. Tare da isasshen aiki, fahimtar waɗannan ra'ayoyin zai zama da sauƙi kuma mafi fahimta.
