Intensity of Light- What factors contribute?

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The intensity of light is influenced by factors such as the number of photons emitted and their energy, which is related to frequency. In the context of the photoelectric effect, light must exceed a certain threshold frequency to emit photoelectrons, regardless of intensity. Increased intensity results in more photons, leading to a higher number of emitted photoelectrons. The equation KE_max = E - φ illustrates that the maximum kinetic energy of ejected electrons is the energy of the absorbed photon minus the energy required to liberate the electron. Photons are indeed considered particles of light, but they are massless quanta of electromagnetic energy.
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Intensity of Light-- What factors contribute?

What factors affect the intensity of light? What is intensity? Are the relationships or equations that link the intensity of light to other variables? I'm asking this because I'm not quite understanding intensity vs. frequency. I'm studying the photoelectric effect and how no photoelectrons are emitted if the light has a frequency lower than the threshold of frequency regardless of how intense the incident radiation was.
 
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Okay, so I've read that increasing the intensity of the incident energy of light gives way to more photons and results in the ejection of more photoelectrons. So the intensity is basically energy? Photons are quantums if EM energy right? So basically the higher intensity a light source has, the more photons it emits and theirfore it results in more photoelectrons being ejected from a metal surface?
 
Can someone explain why KE_{max}=E-\phi given that E=hf and is fixed for all of the photons absorbed by the electrons. I know that the the minimum energy needed to liberate an electron from its atom is \phi but I still don't get why the max KE is equal to E-Phi. Is it because it takes the electron Phi amount of energy to liberate itself and therefore the left over of the absorbed energy E minus Phi would give the energy left after liberation and this energy would equal the KE?
 
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