# Photoelectric effect

## Homework Statement

Lenard's experiment on photoelectric effect concluded mvm2/2 = eVs where vm is the highest velocity of photo electrons and Vs is the stopping potential. From this he concluded maximum velocity of photo electrons depends only on the wavelength of light used and not on the intensity.
But another important conclusion drawn from Lenard's experiment is that photoelectric current is independent of wavelength of light but depends only on the intensity of light.
I am confused. Can someone clarify?

## The Attempt at a Solution

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Photoelectric current is related to how many electrons are ejected, not to their maximum velocity. When you shine a beam of photons on a metal, it is likely that each photon will hit only one electron. In the process, it will transfer all its energy to the electron. This energy is given by E=hf. f is the frequency. or E=hc/L. where L is the wavelength. If this energy is greater than the work function Phi and the electron is on the surface of the metal then it will be ejected.The work function is the minimum energy required to eject a photoelectron i.e. the energy required to eject an electron from the surface. The difference between the work function and the photon energy will give you the max kinetic energy that the photoelectron can have (and thus it's max velocity). Notice that in our discussion to determine the highest velocity we only needed the work function (a constant for every metal) and the photon energy. Photoelectric current, on the other hand, is related to the NUMBER of photoelectrons ejected. If the above story repeats many times, i.e. there are many photons striking many electrons and causing them to be ejected then a higher current will be produced. Note that the current is related to the number of photons striking the metal that have energies greater than the work function. The more photons of this type that you have the more electrons will be ejected and the higher the photoelectric current. Now intensity comes into play. Intensity is the energy transfered per unit area per unit time. So if you have only one type of photons (i mean photons of only one frequency) then to increase the intensity you have to increase the number of photons. ( The other way to increase intensity is to increase the frequency of photons making them carry more energy but this is irrelevant to our discussion since it will increase the max velocity not the current). If you increase the number of photons you will thus get a higher photoelectric current but with the same max velocity.

I hope that helped.

Beautiful explanation mr. gogobeid. I got it now. Thanks a lot

you're most welcome

Let me remind cheekily that all gratefulness be directed to the great Albert Einstein first.

There is one slight problem still occurring...

Agreed that when we increase the intensity of the incident the number of electrons ejected from the metal increases and hence the number of electrons reaching the Collector plate per second increases and hence there will be an increase in the photoelectric current.

but when we increase the frequency, the kinetic energy of the electrons emitted increases and hence their velocity. If their velocity increases the electron will reach the Collector plate faster. hence this will also lead to an increase in the number of electrons reaching the collector plate per second. should this not also lead to an increase in the photoelectric current?

i understand that in lenard's experiment that it was shown that the photoelectric current is constant. but my question is why?

If their velocity increases the electron will reach the Collector plate faster. hence this will also lead to an increase in the number of electrons reaching the collector plate per second. should this not also lead to an increase in the photoelectric current?
I am no expert but since there has not been an answer I believe:

the electrons will get there faster but the NUMBER of them depends on intensity.

frequency determines if and how fast the electron will be moving and intensity determines how much that is happening.

hopefully someone can back this up