What is the relationship between frequency and photocurrent?

Question

I know this question has been posted before but i'm down a rabbit hole as I keep finding different answers to it. My understanding is that photocurrent increases with intensity and decreases with frequency.

Obviously intensity increases current because

"the intensity of light is proportional to the number of photons. If a photon's energy exceeds the work function, there will be more photons incident on the object, causing more photoelectrons to be emitted. When more photoelectrons are emitted and reach the collecting plate, a greater current is observed."

HOWEVER if frequency is increased while keeping the intensity/number of photons constant, then each photon would carry more energy, which means a fewer number of photons would be required to give the same amount of energy, resulting in a smaller photocurrent. I got this understanding from this source https://scienceready.com.au/pages/common-misconception-in-photoelectric-effect-experiments. Basically it explains

"why as the frequency of light varies (with constant intensity), the magnitude of photocurrent does not remain constant"

and the math used in the video checks out.

The video in the link above also showed this question where the physicist used a smaller wavelength (400nm instead of 500nm), which means a larger frequency. The correct answer for that question was higher stopping voltage and smaller photocurrent as you can see:

So basically if you keep the intensity/the number of photons the same, your photocurrent should go down according to the math, right?

I played with this PheT https://phet.colorado.edu/sims/cheerpj/photoelectric/latest/photoelectric.html?simulation=photoelectric, and found that the current did indeed decrease after the threshold frequency. (NOTE: this is due to the settings of the simulation, which is explained in the answer of the following post)

This post explains why the simulation acts the way it does: What is the relationship between photocurrent vs frequency?.

Theres also these two graphs which contradict eachother. I found this one online, which shows that the photocurrent decreased with a lower intensity but same frequency:

and then theres this graph from my textbook which shows the same photocurrent despite increasing frequency:

So what exactly is going on, do textbooks use a simplified model? Does that mean frequency does not change photocurrent, or is that just what the textbook says? Can someone please definitevly explain the relationship between photocurrent and frequency as simply as possible. I'm in highschool btw.

Answer 1

It is possible that the term "Intensity" is causing some vagueness here.

First, it should be emphasized that one photon produces one photoelectron (according to Einstein, as mentioned in the video).

Now, if "intensity" is given in units of $W/m^{2}$, as in the video, then if you have a fixed intensity, increasing the frequency (energy) of the light will result in less photons as explained. Since each photon has higher energy ($E=hf$), it takes less of them to equate to the same $W/m^{2}$. Therefore, reduced photoelectrons/photocurrent.

However, if "intensity" is taken to be the number of photons per second, then as the frequency (energy) of each photon increases, the number of photons will not change if the intensity is kept fixed. Therefore, unchanged photoelectrons/photocurrent.

You may find it useful/interesting to reference the original 1905 paper by Einstein to see the original derivation of the photoelectric effect explanation.