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I assume you are referring to kinetic energy of an electron ejected in a photoelectric effect problem? If you are, the KE is zero when the energy (E=hv) of the incoming light is equal to the work function. In other words, you don't have any excess energy to be released as KE or the wavelength of the incoming light is the longest possible wavelength to eject an electron.
Kinetic energy would be zero if the energy from the electromagnetic radiation was exactly equal to the work function of the metal. E = work function + KE of electrons so if E = work function, kinetic energy would be zero, and the energy of the radiation was just enough to remove the electron and nothing more.
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