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There is kinetic energy when the energy of the photons being aimed at the metal is greater than the work function. Therefore, if the energy of the photon is equal to the work function there is no kinetic energy. The kinetic energy is the excess energy from the photon therefore if there is no excess (they are equal to each other) then there is no kinetic energy.
Kinetic energy is zero when the work function iis equal to the energy of the photon hitting the metal. If a problem asks how much energy is required to eject an electron from a surface of the metal you would also make KE equal to zero.
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