In the photoelectric effect, the energy of the incoming photon (E=hf) is used in part to extract the photoelectron from the metal (work function) and the rest is converted into kinetic energy of the photoelectron:
[tex]hf = \phi + K[/tex]
where
h is the Planck constant
f is the frequency of the incident light
[tex]\phi[/tex] is the work function of the material
K is the kinetic energy of the photoelectron.
The photoelectron generally loses part of its kinetic energy inside the material; however, we are interested in its maximum kinetic energy, that is the one the electron has when it doesn't lose energy, so we can rewrite the previous equation as
[tex]K_{max} = hf - \phi[/tex]
The work function is (in Joule)
[tex]\phi = (4.97 eV)(1.6 \cdot 10^{-19} J/eV)=7.95 \cdot 10^{-19} J[/tex]
and using the data of the problem, we find the maximum kinetic energy of the photoelectrons
[tex]K_{max} = (6.6 \cdot 10^{-34} Js)(1.5 \cdot 10^{15} Hz)-7.95 \cdot 10^{-19}J= 1.95 \cdot 10^{-19} J[/tex]
