In a photoelectric-effect experiment it is observed that no current flows unless the wavelength is less than 560 nm what is the work function of this material?

In the photoelectric effect, the energy of the incoming photon is used in part to extract the photoelectron from the material (work function) and the rest is converted into kinetic energy of the photoelectron:

where
hf is the energy of the incoming photon
h is the Planck constant
f is the light frequency
is the work function of the material
is the maximum kinetic energy of the photoelectrons.

The problem says that no current flows when the wavelength of the light is less than 560 nm. It means that when the wavelength has this value, the maximum kinetic energy of the photoelectrons is zero: , and the energy of the incoming photons is just enough to extract the photoelectrons from the material, so
(1)

The wavelength of the photons is

and we can find the frequency of the light by using the relationship between frequency and wavelength


And by using (1) and the frequency of the photons, we can find the work function of the material: