Mehlala ea Lipotso tse Buisanang ka Phello ea Photoelectric
Tšusumetso ea photoelectric ke ketsahalo ea 'mele e hlalosang ho ntšoa ha lielektrone ho tloha holim'a thepa ha khanya kapa mahlaseli a motlakase a e otla. Lipatlisiso tse entsoeng ke Albert Einstein mathoasong a lekholo la bo20 la lilemo li bapetse karolo ea bohlokoa ho hlaloseng ketsahalo ena le ho lebisa ho amoheloeng ha khopolo-taba ea quantum ea leseli. Sehlooho sena se tla tšohla mehlala e 'maloa ea mathata a amanang le phello ea photoelectric hammoho le litlhaloso tse qaqileng tsa litharollo tsa tsona.
Khopolo-taba ea Motheo
Pele re fetela mathateng a mohlala, a re hlahlobeng likhopolo tse ling tsa motheo tse amanang le phello ea photoelectric:
1. Matla a photon: Matla a photon a fanoa ke equation \( E = h \nu \), moo \( h \) e leng ntho e sa fetoheng ya Planck (\( h \approx 6.626 \times 10^{-34} \) Js) mme \( \nu \) ke maqhubu a lesedi.
2. Mosebetsi oa mosebetsi (\( \phi \)): Mosebetsi oa mosebetsi ke matla a bonyane a hlokahalang ho tlosa lielektrone holim'a thepa.
3. Matla a kinetic a dielektrone: Dielektrone tse lokollotsweng di na le matla a kinetic a fanwang ke equation \( KE = h \nu – \phi \).
Mohlala oa Potso ea 1
Soal
Letlapa la tšepe le na le mosebetsi oa \( 4.5 \) eV. Leseli le nang le bolelele ba leqhubu la \( 200 \) nm lea khanya holim'a letlapa. Fumana:
1. Matla a photon a monngoang ke elektrone.
2. Na dielektrone di tla lokollwa hodima tshepe?
3. Haeba ho joalo, matla a kinetic a phahameng ka ho fetisisa a lielektrone tse lokollotsoeng ke afe?
Penyelesaian
1. Bala matla a photon (\( E \))
\[
E = \frac{hc}{\lambda}
\]
Moo \( h \) e leng ntho e sa fetoheng ya Planck, \( c \) ke lebelo la lesedi (\( c \haufi le 3 \makgetlo a 10^8 \) m/s), mme \( \lambda \) ke bolelele ba leqhubu la lesedi.
\[
E = \frac{6.626 \times 10^{-34} \text{ Js} \times 3 \times 10^8 \text{ m/s}}{200 \times 10^{-9} \text{ m}}
\]
\[
E = \frac{1.9878 \times 10^{-25} \text{ Js}}{200 \times 10^{-9} \text{ m}}
\]
\[
E = 9.939 \makgetlo a 10^{-19} \mongolo{J}
\]
Ho fetolela ho eV, sebedisa \( 1 \text{ eV} = 1.602 \times 10^{-19} \text{ J} \).
\[
E = \frac{9.939 \times 10^{-19} \text{ J}}{1.602 \times 10^{-19} \text{ J/eV}}
\]
\[
E \hoo e ka bang 6.2 \mongolo{eV}
\]
2. Hlahloba hore na dielektrone di tla lokollwa
Hobane matla a photon (6.2 eV) a maholo ho feta mosebetsi oa mosebetsi (4.5 eV), elektrone e tla lokolloa.
3. Bala matla a maholo a kinetic a dielektrone
\[
KE = E – \phi = 6.2 \mongolo{eV} – 4.5 \mongolo{ eV} = 1.7 \mongolo{ eV}
\]
Mohlala oa Potso ea 2
Soal
Leseli le nang le maqhubu a \( 1.2 \makhetlo a 10^{15} \) Hz le khanya holim'a bokaholimo ba tšepe bo nang le mosebetsi oa \( 3 \) eV. Fumana:
1. Matla a photon a monngoang ke elektrone.
2. Na dielektrone di tla lokollwa hodima tshepe?
3. Haeba ho joalo, matla a kinetic a phahameng ka ho fetisisa a lielektrone tse lokollotsoeng ke afe?
Penyelesaian
1. Bala matla a photon (\( E \))
\[
E = h \nu = 6.626 \ka makhetlo a 10^{-34} \mongolo{Js} \ka makhetlo a 1.2 \ka makhetlo a 10^{15} \mongolo{Hz}
\]
\[
E = 7.9512 \makgetlo a 10^{-19} \mongolo{J}
\]
Phetoho ho eV:
\[
E = \frac{7.9512 \times 10^{-19} \text{ J}}{1.602 \times 10^{-19} \text{ J/eV}}
\]
\[
E \hoo e ka bang 4.97 \mongolo{eV}
\]
2. Hlahloba hore na dielektrone di tla lokollwa
Hobane matla a photon (4.97 eV) a maholo ho feta mosebetsi oa mosebetsi (3 eV), elektrone e tla lokolloa.
3. Bala matla a maholo a kinetic a dielektrone
\[
KE = E – \phi = 4.97 \mongolo{eV} – 3 \mongolo{ eV} = 1.97 \mongolo{ eV}
\]
Mohlala oa Potso ea 3
Soal
Leseli la UV le nang le bolelele ba leqhubu ba \( 120 \) nm le otla bokaholimo ba tšepe bo nang le mosebetsi oa \( 2.2 \) eV. Bala:
1. Matla a photon ho eV.
2. Na dielektrone di tla lokollwa hodima tshepe?
3. Haeba ho joalo, matla a kinetic a phahameng ka ho fetisisa a lielektrone tse lokollotsoeng ke afe?
Penyelesaian
1. Bala matla a photon (\( E \))
\[
E = \frac{hc}{\lambda}
\]
\[
E = \frac{6.626 \times 10^{-34} \text{ Js} \times 3 \times 10^8 \text{ m/s}}{120 \times 10^{-9} \text{ m}}
\]
\[
E = \frac{1.9878 \times 10^{-25} \text{ Js}}{120 \times 10^{-9} \text{ m}}
\]
\[
E = 1.6565 \makgetlo a 10^{-18} \mongolo{J}
\]
Phetoho ho eV:
\[
E = \frac{1.6565 \times 10^{-18} \text{ J}}{1.602 \times 10^{-19} \text{ J/eV}}
\]
\[
E \hoo e ka bang 10.34 \mongolo{eV}
\]
2. Hlahloba hore na dielektrone di tla lokollwa
Hobane matla a photon (10.34 eV) a maholo ho feta mosebetsi oa mosebetsi (2.2 eV), elektrone e tla lokolloa.
3. Bala matla a maholo a kinetic a dielektrone
\[
KE = E – \phi = 10.34 \mongolo{eV} – 2.2 \mongolo{ eV} = 8.14 \mongolo{ eV}
\]
Qetello
Ketsahalo ea phello ea photoelectric e ka bontšoa ka mathata a fapaneng a mehlala moo re balang matla a photon, re hlahloba hore na elektrone e ka ntšoa, 'me re lekanya matla a kinetic a phahameng ka ho fetisisa a elektrone e ntšoang. Ha re rarolla bothata bo bong le bo bong, re hloka ho ba hlokolosi ka li-unit tsa 'mele le liphetoho lipakeng tsa li-unit (mohlala, ho tloha ho li-joules ho ea ho li-electronvolts). Kutloisiso e tiileng le mokhoa o nepahetseng li tla re thusa ho tseba likhopolo tsa motheo tsa phello ea photoelectric, e leng tšiea ea bohlokoa ea fisiks ea quantum.
