When ultraviolet light with a wavelength of 400 nm falls on a certain metal surface, the maximum kinetic energy of the emitted photoelectrons is measured to be 1.10 ev . what is the maximum kinetic energy of the photoelectrons when light of wavelength 285 nm falls on the same surface?

In the photoelectric effect, the energy of the incoming photon is used partially to extract the photoelectron from the metal (work function) and the rest is converted into kinetic energy of the photoelectrons:
(1)
where
h is the Planck constant
f is the photon frequency
is the work function
is the maximum kinetic energy of the photoelectrons

In the first part of the problem, we have light with wavelength , so the photons have frequency 

where c is the speed of light; and therefore the energy of the photons is

Converted into electronvolts ():


The maximum kinetic energy of the photoelectrons in this case is 
, so we can find the work function of the metal by re-arranging eq. (1):


In the second part of the problem, we have light with wavelength , which corresponds to a frequency of

And so the photons have energy

which corresponds to 


And if we use again eq.(1), we can now find the new maximum kinetic energy of the photoelectrons: