# Effect of collector plate potential on photoelectric current with varying frequencies?

The above graph is from my physics book which shows the effect of collector plate potential on photoelectric current for different frequencies.

Inference from above graph:

• Since all the three frequency curve have same saturation current,this must imply same intensity for all three as photoelectric current depends on intensity of radiation.
• Intensity equals I=nhv/AT (where A and T is constant),thus intensity depends on both number of photons(n) and frequency of radiation(v).
• Since intensity is constant,this should mean a inverse proportionality relation between number of photon and frequency,As frequency increases number of photon decreases to maintain same intensity.
• But as the number of photon decreases ,number of photoelectron decreases resulting in a decreases in photoelectric current

• Thus concluding that different frequencies should not have same saturation current

• Is this graph right or wrong? Or am I missing something

Self Explanation

• As frequency increases, meaning energy of photon increases thus more energetic photons can free even the tightly bounded electrons. Contributing more photoelectrons,thus increasing photoelectric current.
• Thus on one hand with constrained intensity there was inverse relation between frequency and photoelectric current.On the other hand there is a direct relation between frequency and photoelectric current based on above reasoning.
• Two opposing effects balances and cancels resulting in all three different frequency curves having same saturation current

Yes higher frequencies emit more electrons, and yes there will be less photons at the same intensity.

"The saturation current increases with the increase of the light intensity. It also increases with greater frequencies due to a greater probability of electron emission when collisions happen with higher energy photons."

https://en.m.wikipedia.org/wiki/Photoelectric_effect

You could fill in details of arguments you make, showing how it all balances out to the same saturation current, or you could just say with conservation of energy, the saturation current has to be the same for those frequencies at the same intensity, assuming no significant differences in energy losses to other processes.