When ultraviolet light with a wavelength of 400 nm falls on a certain metal surface, the maximum kinetic energy of the emitted photoelectrons is 1.10 ev . part a what is the maximum kinetic energy k0 of the photoelectrons when light of wavelength 270 nm falls on the same surface?

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

The ultraviolet light has a wavelength of , so its frequency is

And the energy of each photon of this light is


The maximum kinetic energy of the emitted photoelectrons is (converting into Joules)


And so by using equation (1) we can find the work function of the material:


Now we have instead light wavelength  hitting the same surface. The frequency of this light is

and the energy of each photon of this light is


And so we can calculate the new maximum kinetic energy of the photoelectrons by using (1) and the work function we found previously:


And if we want to convert it into electronvolts,
 

The maximum kinetic energy of the photoelectrons has increased because the light hitting the surface is now more energetic, so it can transfer more energy to the electrons.

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