Light of intensity 10^(-5) W m^(-2) falls on a sodium photo-cell of surface area 2 cm^(2) . Assuming that the top 5 layers of sodium absorb the incident energy, estimate time required for photoelectric emission in the wave-picture of radiation. The work function for the metal is given to be about 2 eV. What is the implication of your answer?

Light of intensity 10^(-5) W m^(-2) falls on a sodium photo-cell of su

1.	Light of intensity 10^(-5) W m^(-2) falls on a sodium photo-cell of surface area 2 cm^(2) . Assuming that the top 5 layers of sodium absorb the incident energy, estimate time required for photoelectric emission in the wave-picture of radiation. The work function for the metal is given to be about 2 eV. What is the implication of your answer?
Answer» <html><body><p></p>Solution :<a href="https://interviewquestions.tuteehub.com/tag/assume-384429" style="font-weight:bold;" target="_blank" title="Click to know more about ASSUME">ASSUME</a> one conduction electron per atom. Effective atomic area `~10^(-<a href="https://interviewquestions.tuteehub.com/tag/20-287209" style="font-weight:bold;" target="_blank" title="Click to know more about 20">20</a>)m^(2)` <br/> Number of electrons in 5 layers <br/> `=(5xx2xx10^(-4)m^(2))/(10^(-20)m^(2))=10^(17)` <br/> Incident power <br/> `=10^(-5)Wm^(-2)xx2xx10^(-4)m^(2)=2xx10^(-9)<a href="https://interviewquestions.tuteehub.com/tag/w-729065" style="font-weight:bold;" target="_blank" title="Click to know more about W">W</a>` <br/> In the wave picture, incident power is uniformly absorbed by all the electrons continuously. Consequently, energy absorbed per second per electron <br/> `=2xx10^(-9)//10^(17)=2xx10^(-26)W` <br/> Time required for photoelectric emission <br/> `=2xx1.6xx10^(-19)J//2xx10^(-26)W=1.6xx10^(7)s` <br/> Which is about 0.5 year <br/> Implication: Experimentally, photoelectric emission is observed nearly instantaneously `(~10^(-9) s)`: Thus, the wave picture is in gross disagreement with experiment. In the photon-picture, energy of the radiation is not continuously shared by all the electrons in the top layers. <a href="https://interviewquestions.tuteehub.com/tag/rather-2973755" style="font-weight:bold;" target="_blank" title="Click to know more about RATHER">RATHER</a>, energy comes in discontinuous ‘quanta’. and <a href="https://interviewquestions.tuteehub.com/tag/absorption-15370" style="font-weight:bold;" target="_blank" title="Click to know more about ABSORPTION">ABSORPTION</a> of energy does not take place gradually. A photon is either not absorbed, or absorbed by an electron nearly instantly.</body></html>

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