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The photoelectric experiment consisted of shining light onto a metal surface to measure the energy needed to remove electrons from different metals. Kinetic energy is equal to energy of the photon minus the the energy to remove the electron (work function/threshold energy). This equation illustrates the concept of conservation of energy.
The photoelectric effect is defined as E(Photon) - threshold E = Kinetic energy of the electron. In order for an electron to be ejected and have KE, the E(Photon) has to be greater than the threshold energy of the metal. If the E(Photon) and threshold energy are equal an electron will be removed but will have no KE.
Try to think of it as whatever the difference between the energy of the photon absorbed and the energy actually needed to remove an electron results in the kinetic, left over energy of the photon pushing out the electron at different velocities.
It basically just says that if the energy of the photon is larger than the work function (the energy it takes to remove the electron), that excess will be converted into kinetic energy of the ejected electron. The equation helps to support the idea that light is also a particle, as only photons of large enough energy can eject electrons.
The equation Ek = HV - Φ represents the kinetic energy of the ejected electron. This is determined by finding the initial energy of the photon subtracting the threshold energy of the metal, which is the minimum energy required to eject an electron from the metal.
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