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To my understanding, increasing energy per photon increases the frequency and decreases the wavelength for light. This energy per photon is what allows electrons to surpass the threshold energy and increase an energy level. Increasing the number of photons with insufficient energy only increases the amplitude of the light wave, and, if the energy (determined by frequency) is insufficient to surpass the threshold energy, then the electron will not increase an energy level.
The amount of energy per photon is important in removing electrons. Simply increasing the number of photons does not remove more electrons because each photon still has insufficient energy. However, by increasing the energy of each photon, rather than the number of photons allows each photon to be able to remove an electron.
Increasing *intensity* (aka number of photons) increases the wave amplitude of light but his has no effect on electron removal. Electrons can be removed based on the wavelength and frequency (short wavelength/ high frequency) of the light which is why it has particle like properties. If the photon has enough energy to remove an electron, increasing the intensity *will* impact electron removal. ie; if the intensity of light with a short wavelength/ high frequency capable of removing an electron is doubled, the number of electrons removed will be doubled (it's important to note that this will not double or change the energy of the electron removed)
Increasing the number of photons means increasing the intensity of light, counterintuitively. Only when the energy of each photon is sufficient, can it remove a electron. One photon is responsible for removing an electron, so it is the energy (frequency) counts, not the number of photons.
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