Work function of cathode, visible light

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SUMMARY

The maximum possible work function for a photodetector designed to respond to the entire range of visible light (400 nm - 700 nm) is 1.78 eV or less. Calculations show that at 400 nm, the energy is 3.11 eV, while at 700 nm, it is 1.78 eV. A work function exceeding 3.11 eV prevents electron emission from visible light, while a work function of 1.78 eV allows for electron emission at 700 nm and efficient emission at 400 nm. Therefore, the work function must be capped at 1.78 eV to ensure functionality across the visible spectrum.

PREREQUISITES
  • Understanding of the photoelectric effect
  • Familiarity with energy equations: E = hf = hc/lambda
  • Knowledge of photon energy calculations
  • Basic principles of photodetector design
NEXT STEPS
  • Research the photoelectric effect and its applications in photodetectors
  • Study the relationship between wavelength and photon energy in detail
  • Explore materials with varying work functions for photodetector applications
  • Learn about the design considerations for photodetectors operating in the visible spectrum
USEFUL FOR

Students in physics or engineering, optical engineers, and researchers focused on photodetector technology and the photoelectric effect.

MienTommy
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Homework Statement


You need to design a photodetector that can respond to the entire range of visible light (400 nm - 700 nm). What is the maximum possible work function?

Homework Equations


E = hf = hc/lambda

The Attempt at a Solution


For 400nm, I got E = 3.11 eV
and for 700nm I got 1.78 eV.

The solution is that the maximum work function is 1.78eV or less, and I do not understand why because 3.11eV is beyond the threshold for 400nm light to emit right? So shouldn't the answer be 3.11eV or greater?
 
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If your material has a work function of 3.11 eV, then 400 nm light is barely able to knock out electrons, the 700 nm light at 1.78 eV/photon cannot knock out any electrons.
If your material has a work function of more than 3.11 eV, you cannot release any electrons with visible light.

If your work function is 1.78 eV/photon, then 700 nm light barely manages to release electrons, 400 nm light can do so easily.
 
What is the energy of the emitted electrons for a work function of 3.11 eV with incident light of 700 nm?
 

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