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When the electron absorbs the incoming photon, it is given energy. The energy, allows the electron to move further from the positively charged nucleus, as the energy is converted into movement or kinetic energy. The metal has a certain threshold energy, which means the photons bombarding the metal must match or exceed the threshold energy in order to eject an electron. That is why when the intensity of low frequency light is increased, no electrons are emitted.
Think of the light hitting the metal surface as a bunch of photos with an energy that is determined by its frequency. If there's not enough energy (aka the work function), then no electrons would be emitted.
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