Work function of cathode, visible light

[MienTommy]

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?

 

[mfb]

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.

 

[J Hann]

What is the energy of the emitted electrons for a work function of 3.11 eV with incident light of 700 nm?