Frequency and intensity in photoelectric effect In the explanation of photoelectric effect it is written that intensity and frequency of radiation have different results i.e. higher intensity means greater number of emitted photoelectrons and higher frequency means greater kinetic energy of emitted photoelectrons.
But what we have learned about intensity is that it is the energy released per unit area per unit time.
So if we say about the intensity of light in terms of photons it would look like this :
I = nhf/area/time.
If we take area to be 1 unit and time to be 1 second then the equation will look like this :
I = nhf
The equations above show that with fixed intensity if frequency is increased then number of photons or say photoelectrons decreases and vice versa. But according to Einstein's theory number of photoelectrons is affected only by the intensity of light not its frequency.
What's the cause of this contradiction ?? Is it okay to define intensity only as number of photons ??
Am I wrong somewhere ?
I am just a beginner so please cooperate.
 A: What you just discovered is that if you keep the intensity of a light source constant and increased the frequency, the number of photons per unit area must decrease. What Einstein told us is that intensity alone is not enough to tell us whether an electron will be ejected from a solid. Increasing the intensity and keeping the frequency constant only increase the number of ejected electrons, and if there are no electrons ejected then nothing happen, none start coming out. However changing the frequency of of the light (even when intensity is kept constant) cause the electrons come out with higher energies.
A: Intensity, in a manner of speaking, is how bright the source of light is. Brighter being more intense.
What Einstein postulated (inspired by Planck) was that light was made up of packets of energy $\epsilon$ (proportional to frequency but we’ll get to that later). So Einstein said if the total energy of a monochromatic light source that you observe per unit area per unit time (intensity) is $E$, then it is made up of $n$ photons. Where n is given by:
$$n=\frac{E}{\epsilon}$$
Note that $\epsilon$ is a property of individual packets of light where as intensity $E$ is only defined for a collection of such packets.
Each packet can knock out one electron from the metal provided it has energy $\epsilon$ greater than the binding energy of the electron historically known as the work function $\phi_0$. The ejected electrons then have the kinetic energy $\epsilon - \phi_0$
Now if we were to increase the brightness of our source, we would be increasing the intensity $E$. Since $\epsilon$ is still the same (as it is the same source), our equation above says that we’ll have a bigger $n$. This means more electrons will be ejected.
Now coming to your question:

I = nhf
In both the equations we see that intensity and frequency are related. But in Einstein's theory both have different results.

It is further seen that the individual energy packets $\epsilon$ are related to frequency as $\epsilon=hf$.
Now, say we have a light source with intensity $E=100$ and the work function $\phi_0=1$. Consider the following two cases:

*

*$\epsilon=10$

*$\epsilon=50$
Both cases there’ll be ejection of electrons. However the number or electrons ejected aren’t the same. In the first case there will be $n=10$ electrons each with kinetic energy of $9$ units. In the second case, only $n=2$ electrons will be ejected albeit with a much higher kinetic energy of $49$ units.
Now let us double the brightness in the same experimental setup. So we have $E=200$ and $\phi_0=1$. Same two cases of:

*

*$\epsilon=10$

*$\epsilon=50$
Again in both cases there’ll be ejection of electrons. In the first case there will be $n=20$ electrons each with kinetic energy of $9$ units, same as before. In the second case, only $n=4$ electrons will be ejected albeit with a much higher kinetic energy of $49$ units, same as before.
What we observe is that the kinetic energy of each ejected electron is unchanged with changing intensity. However the number of ejected electrons has doubled with doubling intensity.
A: Whatever you have said is right but only one thing wrong. "But according to Einstein's theory number of photoelectrons is affected only by the intensity of light not its frequency." That's is not in Einstein's theory. You can check it in any book. It is written as "The photocurrent increases if the intensity of
the incident light is increased". Einstein have not said anything about when the intensity is fixed but the frequency is changed.
