Zitsanzo za Mafunso Okhudza Mphamvu ya Photoelectric
Mphamvu ya kuwala kwa dzuwa ndi chinthu chomwe chimafotokoza kutuluka kwa ma elekitironi kuchokera pamwamba pa chinthu pamene kuwala kapena mphamvu yamagetsi ikuchigunda. Kafukufuku wochitidwa ndi Albert Einstein kumayambiriro kwa zaka za m'ma 20 adagwira ntchito yofunika kwambiri pofotokoza izi ndikutsogolera kuvomereza chiphunzitso cha quantum cha kuwala. Nkhaniyi ikambirana zitsanzo zingapo za mavuto okhudzana ndi mphamvu ya kuwala kwa dzuwa pamodzi ndi kufotokozera mwatsatanetsatane mayankho awo.
Chiphunzitso Choyambira
Tisanapite ku mavuto a chitsanzo, tiyeni tiwone mfundo zina zofunika zokhudzana ndi mphamvu ya photoelectric:
1. Mphamvu ya photon: Mphamvu ya photon imaperekedwa ndi equation \( E = h \nu \), pomwe \( h \) ndi chosasintha cha Planck (\( h \pafupifupi 6.626 \times 10^{-34} \) Js) ndipo \( \nu \) ndi kuchuluka kwa kuwala.
2. Ntchito ya ntchito (\( \phi \)): Ntchito ya ntchito ndi mphamvu yochepa yomwe imafunika kuchotsa ma elekitironi pamwamba pa chinthucho.
3. Mphamvu ya kinetic ya ma elekitironi: Ma elekitironi otulutsidwa ali ndi mphamvu ya kinetic yoperekedwa ndi equation \( KE = h \nu – \phi \).
Chitsanzo cha Funso 1
Funso
Chipepala chachitsulo chili ndi ntchito ya \( 4.5 \) eV. Kuwala kokhala ndi mafunde a \( 200 \) nm kumawala papepala. Dziwani:
1. Mphamvu ya photon yomwe imatengedwa ndi elekitironi.
2. Kodi ma elekitironi adzatulutsidwa pamwamba pa chitsulo?
3. Ngati inde, kodi mphamvu yayikulu ya kinetic ya ma elekitironi otulutsidwa ndi iti?
Penyelesaian
1. Werengani mphamvu ya photon (\( E \))
\[
E = \frac{hc}{\lambda}
\]
Pamene \( h \) ndi chosasintha cha Planck, \( c \) ndi liwiro la kuwala (\( c \pafupifupi 3 \times 10^8 \) m/s), ndipo \( \lambda \) ndi kutalika kwa mafunde a kuwala.
\[
E = \frac{6.626 \times 10^{-34} \text{ Js} \times 3 \times 10^8 \text{ m/s}}{200 \times 10^{-9} \text{ m}}
\]
\[
E = \frac{1.9878 \times 10^{-25} \text{ Js}}{200 \times 10^{-9} \text{ m}}
\]
\[
E = 9.939 \nthawi 10^{-19} \malemba{ J}
\]
Kuti musinthe kukhala eV, gwiritsani ntchito \( 1 \text{ eV} = 1.602 \times 10^{-19} \text{ J} \).
\[
E = \frac{9.939 \times 10^{-19} \text{ J}}{1.602 \times 10^{-19} \text{ J/eV}}
\]
\[
E \pafupifupi 6.2 \text{ eV}
\]
2. Onani ngati ma elekitironi adzatulutsidwa
Chifukwa mphamvu ya photon (6.2 eV) ndi yayikulu kuposa ntchito yogwirira ntchito (4.5 eV), electron idzatulutsidwa.
3. Werengani mphamvu yayikulu ya kinetic ya ma elekitironi
\[
KE = E – \phi = 6.2 \mawu{eV} – 4.5 \mawu{eV} = 1.7 \mawu{eV}
\]
Chitsanzo cha Funso 2
Funso
Kuwala komwe kumakhala ndi ma frequency a \( 1.2 \times 10^{15} \) Hz kumawala pamwamba pa chitsulo chomwe chili ndi ntchito ya \( 3 \) eV. Dziwani:
1. Mphamvu ya photon yomwe imatengedwa ndi elekitironi.
2. Kodi ma elekitironi adzatulutsidwa pamwamba pa chitsulo?
3. Ngati inde, kodi mphamvu yayikulu ya kinetic ya ma elekitironi otulutsidwa ndi iti?
Penyelesaian
1. Werengani mphamvu ya photon (\( E \))
\[
E = h \nu = 6.626 \nthawi 10^{-34} \malemba{ Js} \nthawi 1.2 \nthawi 10^{15} \malemba{ Hz}
\]
\[
E = 7.9512 \nthawi 10^{-19} \malemba{ J}
\]
Kusintha kukhala eV:
\[
E = \frac{7.9512 \times 10^{-19} \text{ J}}{1.602 \times 10^{-19} \text{ J/eV}}
\]
\[
E \pafupifupi 4.97 \text{ eV}
\]
2. Onani ngati ma elekitironi adzatulutsidwa
Chifukwa mphamvu ya photon (4.97 eV) ndi yayikulu kuposa ntchito yogwirira ntchito (3 eV), electron idzatulutsidwa.
3. Werengani mphamvu yayikulu ya kinetic ya ma elekitironi
\[
KE = E – \phi = 4.97 \mawu{eV} – 3 \mawu{eV} = 1.97 \mawu{eV}
\]
Chitsanzo cha Funso 3
Funso
Kuwala kwa UV komwe kumakhala ndi kutalika kwa mafunde a \( 120 \) nm kumagunda pamwamba pa chitsulo chomwe chili ndi ntchito ya \( 2.2 \) eV. Werengani:
1. Mphamvu ya photon mu eV.
2. Kodi ma elekitironi adzatulutsidwa pamwamba pa chitsulo?
3. Ngati inde, kodi mphamvu yayikulu ya kinetic ya ma elekitironi otulutsidwa ndi iti?
Penyelesaian
1. Werengani mphamvu ya photon (\( E \))
\[
E = \frac{hc}{\lambda}
\]
\[
E = \frac{6.626 \times 10^{-34} \text{ Js} \times 3 \times 10^8 \text{ m/s}}{120 \times 10^{-9} \text{ m}}
\]
\[
E = \frac{1.9878 \times 10^{-25} \text{ Js}}{120 \times 10^{-9} \text{ m}}
\]
\[
E = 1.6565 \nthawi 10^{-18} \malemba{ J}
\]
Kusintha kukhala eV:
\[
E = \frac{1.6565 \times 10^{-18} \text{ J}}{1.602 \times 10^{-19} \text{ J/eV}}
\]
\[
E \pafupifupi 10.34 \text{ eV}
\]
2. Onani ngati ma elekitironi adzatulutsidwa
Chifukwa mphamvu ya photon (10.34 eV) ndi yayikulu kuposa ntchito yogwirira ntchito (2.2 eV), electron idzatulutsidwa.
3. Werengani mphamvu yayikulu ya kinetic ya ma elekitironi
\[
KE = E – \phi = 10.34 \mawu{eV} – 2.2 \mawu{eV} = 8.14 \mawu{eV}
\]
Mapeto
Chochitika cha photoelectric effect chingafotokozedwe kudzera mu zitsanzo zosiyanasiyana za mavuto pomwe timawerengera mphamvu ya photon, kuwona ngati elekitironi ikhoza kutulutsidwa, ndikuyesa mphamvu yayikulu ya kinetic ya elekitironi yotulutsidwa. Pothetsa vuto lililonse, tiyenera kusamala ndi mayunitsi enieni ndi kusintha pakati pa mayunitsi (monga, kuchokera ku ma joules kupita ku ma electronvolts). Kumvetsetsa bwino komanso machitidwe oyenera kudzatithandiza kudziwa bwino mfundo zazikulu za photoelectric effect, yomwe ndi mzati wofunikira wa quantum physics.
