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If a photon has an energy equals the work function, the photon energy can be transferred to the electron and the electron will have enough energy to escape from the metal. The kinetic energy will be zero.
Unless the E(Photon) is greater than or equal to the E(Energy to remove an electron), an electron will not be emitted even for HIGH INTENSITY light, which was quite unexpected in the photoelectric effect experiment. Light sources with long wavelength (low frequency) light does not eject electrons even with this high intensity light.
When energy of the photo is equal to energy of the work function the electron will still get ejected since the energy of the photon reaches the threshold energy, which is the minimum amount of energy needed to remove an electron from the metal surface. I was confused at this concept too of ejected electrons having KE=0, but my guess is that since the detector has a slightly positive charge it draws the ejected electron towards it even when KE=0.
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