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:
[tex]hf=\phi + K_{max}[/tex]
where
hf is the energy of the incoming photon
h is the Planck constant
f is the light frequency
[tex]\phi[/tex] is the work function of the material
[tex]K_{max}[/tex] 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: [tex]K_{max}=0[/tex], and the energy of the incoming photons is just enough to extract the photoelectrons from the material, so
[tex]hf=\phi[/tex] (1)
The wavelength of the photons is
[tex]\lambda=560 nm=560 \cdot 10^{-9} m[/tex]
and we can find the frequency of the light by using the relationship between frequency and wavelength
[tex]f= \frac{c}{\lambda}= \frac{3 \cdot 10^8 m/s}{560 \cdot 10^{-9} m} =5.36 \cdot 10^{14} Hz [/tex]
And by using (1) and the frequency of the photons, we can find the work function of the material:
[tex]\phi=hf=(6.6 \cdot 10^{-34} Js)(5.36\cdot 10^{14} Hz)=3.54 \cdot 10^{-19} J[/tex]
